@article{binswanger_hoefer_ilan_sprenger_2021, title={Whitham modulation theory for generalized Whitham equations and a general criterion for modulational instability}, ISSN={["1467-9590"]}, DOI={10.1111/sapm.12398}, abstractNote={Abstract}, journal={STUDIES IN APPLIED MATHEMATICS}, author={Binswanger, Adam L. and Hoefer, Mark A. and Ilan, Boaz and Sprenger, Patrick}, year={2021}, month={May} }
 @article{congy_el_hoefer_shearer_2018, title={Nonlinear Schrödinger equations and the universal description of dispersive shock wave structure}, volume={142}, ISSN={0022-2526}, url={http://dx.doi.org/10.1111/sapm.12247}, DOI={10.1111/sapm.12247}, abstractNote={Abstract}, number={3}, journal={Studies in Applied Mathematics}, publisher={Wiley}, author={Congy, T. and El, G.A. and Hoefer, M.A. and Shearer, M.}, year={2018}, month={Nov}, pages={241–268} }
 @article{shearer_el_hoefer_2017, title={Stationary Expansion Shocks for a Regularized Boussinesq System}, volume={139}, ISSN={0022-2526}, url={http://dx.doi.org/10.1111/sapm.12191}, DOI={10.1111/sapm.12191}, abstractNote={Abstract}, number={4}, journal={Studies in Applied Mathematics}, publisher={Wiley}, author={Shearer, Michael and El, Gennady A. and Hoefer, Mark A.}, year={2017}, month={Sep}, pages={1–22} }
 @article{maiden_bookman_hoefer_2014, title={Attraction, merger, reflection, and annihilation in magnetic droplet soliton scattering}, volume={89}, ISSN={["1550-235X"]}, DOI={10.1103/physrevb.89.180409}, abstractNote={The interaction behavior of solitons are defining characteristics of these nonlinear, coherent structures. Due to recent experimental observations, thin ferromagnetic films offer a promising medium in which to study the scattering properties of two-dimensional magnetic droplet solitons, particle-like, precessing dipoles. Here, a rich set of two-droplet interaction behaviors are classified through micromagnetic simulations. Repulsive and attractive interaction dynamics are generically determined by the relative phase and speeds of the two droplets and can be classified into four types: (1) merger into a breather bound state, (2) counterpropagation trapped along the axis of symmetry, (3) reflection, and (4) violent droplet annihilation into spin wave radiation and a breather. Utilizing a nonlinear method of images, it is demonstrated that these dynamics describe repulsive/attractive scattering of a single droplet off of a magnetic boundary with pinned/free spin boundary conditions, respectively. These results explain the mechanism by which propagating and stationary droplets can be stabilized in a confined ferromagnet.}, number={18}, journal={PHYSICAL REVIEW B}, author={Maiden, M. D. and Bookman, L. D. and Hoefer, M. A.}, year={2014}, month={May} }
 @article{iacocca_dumas_bookman_mohseni_chung_hoefer_akerman_2014, title={Confined Dissipative Droplet Solitons in Spin-Valve Nanowires with Perpendicular Magnetic Anisotropy}, volume={112}, ISSN={["1079-7114"]}, DOI={10.1103/physrevlett.112.047201}, abstractNote={Magnetic dissipative droplets are localized, strongly nonlinear dynamical modes excited in nanocontact spin valves with perpendicular magnetic anisotropy. These modes find potential application in nanoscale structures for magnetic storage and computation, but dissipative droplet studies have so far been limited to extended thin films. Here, numerical and asymptotic analyses are used to demonstrate the existence and properties of novel solitons in confined structures. As a nanowire's width is decreased with a nanocontact of fixed size at its center, the observed modes undergo transitions from a fully localized two-dimensional droplet into a two-dimensional droplet edge mode and then a pulsating one-dimensional droplet. These solitons are interpreted as dissipative versions of classical, conservative solitons, allowing for an analytical description of the modes and the mechanisms of bifurcation. The presented results open up new possibilities for the study of low-dimensional solitons and droplet applications in nanostructures.}, number={4}, journal={PHYSICAL REVIEW LETTERS}, author={Iacocca, Ezio and Dumas, Randy K. and Bookman, Lake and Mohseni, Majid and Chung, Sunjae and Hoefer, Mark A. and Akerman, Johan}, year={2014}, month={Jan} }
 @article{lowman_hoefer_el_2014, title={Interactions of large amplitude solitary waves in viscous fluid conduits}, volume={750}, ISSN={["1469-7645"]}, DOI={10.1017/jfm.2014.273}, abstractNote={Abstract}, journal={JOURNAL OF FLUID MECHANICS}, author={Lowman, Nicholas K. and Hoefer, M. A. and El, G. A.}, year={2014}, month={Jul}, pages={372–384} }
 @article{hoefer_2014, title={Shock Waves in Dispersive Eulerian Fluids}, volume={24}, ISSN={["1432-1467"]}, DOI={10.1007/s00332-014-9199-4}, abstractNote={The long-time behavior of an initial step resulting in a dispersive shock wave (DSW) for the one-dimensional isentropic Euler equations regularized by generic, third-order dispersion is considered by use of Whitham averaging. Under modest assumptions, the jump conditions (DSW locus and speeds) for admissible, weak DSWs are characterized and found to depend only upon the sign of dispersion (convexity or concavity) and a general pressure law. Two mechanisms leading to the breakdown of this simple wave DSW theory for sufficiently large jumps are identified: a change in the sign of dispersion, leading to gradient catastrophe in the modulation equations, and the loss of genuine nonlinearity in the modulation equations. Large amplitude DSWs are constructed for several particular dispersive fluids with differing pressure laws modeled by the generalized nonlinear Schrödinger equation. These include superfluids (Bose–Einstein condensates and ultracold fermions) and “optical fluids.” Estimates of breaking times for smooth initial data and the long-time behavior of the shock tube problem are presented. Detailed numerical simulations compare favorably with the asymptotic results in the weak to moderate amplitude regimes. Deviations in the large amplitude regime are identified with breakdown of the simple wave DSW theory.}, number={3}, journal={JOURNAL OF NONLINEAR SCIENCE}, author={Hoefer, M. A.}, year={2014}, month={Jun}, pages={525–577} }
 @article{chung_mohseni_sani_iacocca_dumas_nguyen_pogoryelov_muduli_eklund_hoefer_et al._2014, title={Spin transfer torque generated magnetic droplet solitons (invited)}, volume={115}, ISSN={["1089-7550"]}, DOI={10.1063/1.4870696}, abstractNote={We present recent experimental and numerical advancements in the understanding of spin transfer torque generated magnetic droplet solitons. The experimental work focuses on nano-contact spin torque oscillators (NC-STOs) based on orthogonal (pseudo) spin valves where the Co fixed layer has an easy-plane anisotropy, and the [Co/Ni] free layer has a strong perpendicular magnetic anisotropy. The NC-STO resistance and microwave signal generation are measured simultaneously as a function of drive current and applied perpendicular magnetic field. Both exhibit dramatic transitions at a certain current dependent critical field value, where the microwave frequency drops 10 GHz, modulation sidebands appear, and the resistance exhibits a jump, while the magnetoresistance changes sign. We interpret these observations as the nucleation of a magnetic droplet soliton with a large fraction of its magnetization processing with an angle greater than 90°, i.e., around a direction opposite that of the applied field. This interpretation is corroborated by numerical simulations. When the field is further increased, we find that the droplet eventually collapses under the pressure from the Zeeman energy.}, number={17}, journal={JOURNAL OF APPLIED PHYSICS}, author={Chung, S. and Mohseni, S. M. and Sani, S. R. and Iacocca, E. and Dumas, R. K. and Nguyen, T. N. Anh and Pogoryelov, Ye and Muduli, P. K. and Eklund, A. and Hoefer, M. and et al.}, year={2014}, month={May} }
 @article{bookman_hoefer_2013, title={Analytical theory of modulated magnetic solitons}, volume={88}, ISSN={["1550-235X"]}, DOI={10.1103/physrevb.88.184401}, abstractNote={Droplet solitons are coherently precessing solitary waves that have been recently realized in thin ferromagnets with perpendicular anisotropy.In the strongly nonlinear regime, droplets can be well approximated by a slowly precessing, circular domain wall with a hyperbolic tangent form. Utilizing this representation, this work develops a general droplet modulation theory and applies it to study the long range effects of the magnetostatic field and a nanocontact spin torque oscillator (NC-STO) where spin polarized currents act as a gain source to counteract magnetic damping. An analysis of the dynamical equations for the droplet's center, frequency and phase demonstrates a negative processional frequency shift due to long range dipolar interactions, dependent on film thickness. Further analysis also demonstrates the onset of a saddle-node bifurcation at the minimum sustaining current for the NC-STO. The basin of attraction associated with the stable node demonstrates that spin torque enacts a restoring force to excursions of the droplet from the nanocontact center, observed previously in numerical simulations. Large excursions lead to the droplet's eventual decay into spin waves.}, number={18}, journal={PHYSICAL REVIEW B}, author={Bookman, L. D. and Hoefer, M. A.}, year={2013}, month={Nov} }
 @article{lowman_hoefer_2013, title={Dispersive hydrodynamics in viscous fluid conduits}, volume={88}, ISSN={["1550-2376"]}, DOI={10.1103/physreve.88.023016}, abstractNote={The evolution of the interface separating a conduit of light, viscous fluid rising buoyantly through a heavy, more viscous, exterior fluid at small Reynolds numbers is governed by the interplay between nonlinearity and dispersion. Previous authors have proposed an approximate model equation based on physical arguments, but a precise theoretical treatment for this two-fluid system with a free boundary is lacking. Here, a derivation of the interfacial equation via a multiple scales, perturbation technique is presented. Perturbations about a state of vertically uniform, laminar conduit flow are considered in the context of the Navier-Stokes equations with appropriate boundary conditions. The ratio of interior to exterior viscosities is the small parameter used in the asymptotic analysis, which leads systematically to a maximal balance between buoyancy driven, nonlinear self-steepening and viscous, interfacial stress induced, nonlinear dispersion. This results in a scalar, nonlinear partial differential equation describing large amplitude dynamics of the cross-sectional area of the intrusive fluid conduit, in agreement with previous derivations. The leading order behavior of the two-fluid system is completely characterized in terms of the interfacial dynamics. The regime of model validity is characterized and shown to agree with previous experimental studies. Viscous fluid conduits provide a robust setting for the study of nonlinear, dispersive wave phenomena.}, number={2}, journal={PHYSICAL REVIEW E}, author={Lowman, N. K. and Hoefer, M. A.}, year={2013}, month={Aug} }
 @article{lowman_hoefer_2013, title={Dispersive shock waves in viscously deformable media}, volume={718}, ISSN={["1469-7645"]}, DOI={10.1017/jfm.2012.628}, abstractNote={Abstract}, journal={JOURNAL OF FLUID MECHANICS}, author={Lowman, Nicholas K. and Hoefer, M. A.}, year={2013}, month={Mar}, pages={524–557} }
 @article{lowman_hoefer_2013, title={Fermionic shock waves: Distinguishing dissipative versus dispersive regularizations}, volume={88}, ISSN={["1094-1622"]}, DOI={10.1103/physreva.88.013605}, abstractNote={The collision of two clouds of Fermi gas at unitarity (UFG) has been recently observed to lead to shock waves whose regularization mechanism, dissipative or dispersive, is being debated. While classical, dissipative shocks, as in gas dynamics, develop a steep, localized shock front that translates at a well-defined speed, dispersively regularized shocks are distinguished by an expanding region of short wavelength oscillations with two speeds, those of the leading and trailing edges. For typical UFG experimental conditions, the theoretical oscillation length scale is smaller than the resolution of present imaging systems so it is unclear how to determine the shock type from its structure alone. Two experimental methods to determine the appropriate regularization mechanism are proposed: measurement of the shock speed and observation of a one-dimensional collision experiment with sufficiently tight radial confinement.}, number={1}, journal={PHYSICAL REVIEW A}, author={Lowman, N. K. and Hoefer, M. A.}, year={2013}, month={Jul} }
 @article{mohseni_sani_persson_nguyen_chung_pogoryelov_muduli_iacocca_eklund_dumas_et al._2013, title={Spin Torque-Generated Magnetic Droplet Solitons}, volume={339}, ISSN={["0036-8075"]}, DOI={10.1126/science.1230155}, abstractNote={Magnetic Droplet}, number={6125}, journal={SCIENCE}, author={Mohseni, S. M. and Sani, S. R. and Persson, J. and Nguyen, T. N. Anh and Chung, S. and Pogoryelov, Ye. and Muduli, P. K. and Iacocca, E. and Eklund, A. and Dumas, R. K. and et al.}, year={2013}, month={Mar}, pages={1295–1298} }
 @article{yan_chang_hamner_hoefer_kevrekidis_engels_achilleos_frantzeskakis_cuevas_2012, title={Beating dark-dark solitons in Bose-Einstein condensates}, volume={45}, ISSN={["1361-6455"]}, DOI={10.1088/0953-4075/45/11/115301}, abstractNote={Motivated by recent experimental results, we study beating dark–dark (DD) solitons as a prototypical coherent structure that emerges in two-component Bose–Einstein condensates. We showcase their connection to dark–bright solitons via SO(2) rotation, and infer from it both their intrinsic beating frequency and their frequency of oscillation inside a parabolic trap. We identify them as exact periodic orbits in the Manakov limit of equal inter- and intra-species nonlinearity strengths with and without the trap and showcase the persistence of such states upon weak deviations from this limit. We also consider large deviations from the Manakov limit illustrating that this breathing state may be broken apart into dark–anti-dark soliton states. Finally, we consider the dynamics and interactions of two beating DD solitons in the absence and in the presence of the trap, inferring their typically repulsive interaction.}, number={11}, journal={JOURNAL OF PHYSICS B-ATOMIC MOLECULAR AND OPTICAL PHYSICS}, author={Yan, D. and Chang, J. J. and Hamner, C. and Hoefer, M. and Kevrekidis, P. G. and Engels, P. and Achilleos, V. and Frantzeskakis, D. J. and Cuevas, J.}, year={2012}, month={Jun} }
 @article{hoefer_ilan_2012, title={DARK SOLITONS, DISPERSIVE SHOCK WAVES, AND TRANSVERSE INSTABILITIES}, volume={10}, ISSN={["1540-3467"]}, DOI={10.1137/110834822}, abstractNote={The nature of transverse instabilities of dark solitons for the (2+1)-dimensional defocusing nonlinear Schrodinger/Gross–Pitaevskii˘ (NLS/GP) equation is considered. Special attention is given to the small (shallow) amplitude regime, which limits to the Kadomtsev–Petviashvili (KP) equation. We study analytically and numerically the eigenvalues of the linearized NLS/GP equation. The dispersion relation for shallow solitons is obtained asymptotically beyond the KP limit. This yields (1) the maximal growth rate and associated wavenumber of unstable perturbations and (2) the separatrix between convective and absolute instabilities. The instability properties of the dark soliton are directly related to those of oblique dispersive shock wave (DSW) solutions. Stationary and nonstationary oblique DSWs are constructed analytically and investigated numerically by direct simulations of the NLS/GP equation. It is found that stationary and nonstationary oblique DSWs have the same jump conditions in the shallow and hyp...}, number={2}, journal={MULTISCALE MODELING & SIMULATION}, author={Hoefer, M. A. and Ilan, B.}, year={2012}, pages={306–341} }
 @article{hoefer_sommacal_2012, title={Propagating two-dimensional magnetic droplets}, volume={241}, ISSN={["0167-2789"]}, DOI={10.1016/j.physd.2012.02.003}, abstractNote={Propagating, solitary magnetic wave solutions of the Landau-Lifshitz equation with uniaxial, easy-axis anisotropy in thin (two-dimensional) magnetic films are investigated. These localized, nontopological wave structures, parametrized by their precessional frequency and propagation speed, extend the stationary, coherently precessing "magnon droplet" to the moving frame, a non-trivial generalization due to the lack of Galilean invariance. Propagating droplets move on a spin wave background with a nonlinear droplet dispersion relation that yields a limited range of allowable droplet speeds and frequencies. An iterative numerical technique is used to compute the propagating droplet's structure and properties. The results agree with previous asymptotic calculations in the weakly nonlinear regime. Furthermore, an analytical criterion for the droplet's orbital stability is confirmed. Time-dependent numerical simulations further verify the propagating droplet's robustness to perturbation when its frequency and speed lie within the allowable range.}, number={9}, journal={PHYSICA D-NONLINEAR PHENOMENA}, author={Hoefer, M. A. and Sommacal, M.}, year={2012}, month={May}, pages={890–901} }
 @article{hoefer_sommacal_silva_2012, title={Propagation and control of nanoscale magnetic-droplet solitons}, volume={85}, ISSN={["1550-235X"]}, DOI={10.1103/physrevb.85.214433}, abstractNote={The propagation and controlled manipulation of strongly nonlinear, two-dimensional solitonic states in a thin, anisotropic ferromagnet are theoretically demonstrated. It has been recently proposed that spin-polarized currents in a nanocontact device could be used to nucleate a stationary dissipative droplet soliton. Here, an external magnetic field is introduced to accelerate and control the propagation of the soliton in a lossy medium. Soliton perturbation theory corroborated by two-dimensional micromagnetic simulations predicts several intriguing physical effects, including the acceleration of a stationary soliton by a magnetic field gradient, the stabilization of a stationary droplet by a uniform control field in the absence of spin torque, and the ability to control the soliton's speed by use of a time-varying, spatially uniform external field. Soliton propagation distances approach 10 $\mu$m in low loss media, suggesting that droplet solitons could be viable information carriers in future spintronic applications, analogous to optical solitons in fiber optic communications.}, number={21}, journal={PHYSICAL REVIEW B}, author={Hoefer, M. A. and Sommacal, M. and Silva, T. J.}, year={2012}, month={Jun} }
 @article{hoefer_weinstein_2011, title={DEFECT MODES AND HOMOGENIZATION OF PERIODIC SCHRODINGER OPERATORS}, volume={43}, ISSN={["1095-7154"]}, DOI={10.1137/100807302}, abstractNote={We consider the discrete eigenvalues of the operator He = − Δ+ V (x )+ e2Q(ex), where V (x) is periodic and Q(y) is localized on R d , d ≥ 1. For e> 0 and sufficiently small, discrete eigenvalues may bifurcate (emerge) from spectral band edges of the periodic Schrodinger operator, H0 = −Δx + V (x), into spectral gaps. The nature of the bifurcation depends on the homogenized Schrodinger operator LA,Q = −∇y · A∇y + Q(y). Here, A denotes the inverse effective mass matrix, associated with the spectral band edge, which is the site of the bifurcation.}, number={2}, journal={SIAM JOURNAL ON MATHEMATICAL ANALYSIS}, author={Hoefer, M. A. and Weinstein, M. I.}, year={2011}, pages={971–996} }
 @article{hoefer_chang_hamner_engels_2011, title={Dark-dark solitons and modulational instability in miscible two-component Bose-Einstein condensates}, volume={84}, ISSN={["1094-1622"]}, DOI={10.1103/physreva.84.041605}, abstractNote={We investigate the dynamics of two miscible superfluids experiencing fast counterflow in a narrow channel. The superfluids are formed by two distinguishable components of a trapped dilute-gas Bose-Einstein condensate (BEC). The onset of counterflow-induced modulational instability throughout the cloud is observed and shown to lead to the proliferation of dark-dark vector solitons. These solitons do not exist in single-component systems, exhibit intriguing beating dynamics, and can experience a transverse instability leading to vortex line structures. Experimental results and multidimensional numerical simulations are presented.}, number={4}, journal={PHYSICAL REVIEW A}, author={Hoefer, M. A. and Chang, J. J. and Hamner, C. and Engels, P.}, year={2011}, month={Oct} }
 @article{hamner_chang_engels_hoefer_2011, title={Generation of Dark-Bright Soliton Trains in Superfluid-Superfluid Counterflow}, volume={106}, ISSN={["1079-7114"]}, DOI={10.1103/physrevlett.106.065302}, abstractNote={The dynamics of two penetrating superfluids exhibit an intriguing variety of nonlinear effects. Using two distinguishable components of a Bose-Einstein condensate, we investigate the counterflow of two superfluids in a narrow channel. We present the first experimental observation of trains of dark-bright solitons generated by the counterflow. Our observations are theoretically interpreted by three-dimensional numerical simulations for the coupled Gross-Pitaevskii equations and the analysis of a jump in the two relatively flowing components' densities. Counterflow-induced modulational instability for this miscible system is identified as the central process in the dynamics.}, number={6}, journal={PHYSICAL REVIEW LETTERS}, author={Hamner, C. and Chang, J. J. and Engels, P. and Hoefer, M. A.}, year={2011}, month={Feb} }
 @article{tovbis_hoefer_2011, title={Semiclassical dynamics of quasi-one-dimensional, attractive Bose-Einstein condensates}, volume={375}, ISSN={["1873-2429"]}, DOI={10.1016/j.physleta.2010.12.009}, abstractNote={The strongly interacting regime for attractive Bose–Einstein condensates (BECs) tightly confined in an extended cylindrical trap is studied. For appropriately prepared, non-collapsing BECs, the ensuing dynamics are found to be governed by the one-dimensional focusing Nonlinear Schrödinger equation (NLS) in the semiclassical (small dispersion) regime. In spite of the modulational instability of this regime, some mathematically rigorous results on the strong asymptotics of the semiclassical limiting solutions were obtained recently. Using these results, “implosion-like” and “explosion-like” events are predicted whereby an initial hump focuses into a sharp spike which then expands into rapid oscillations. Seemingly related behavior has been observed in three-dimensional experiments and models, where a BEC with a sufficient number of atoms undergoes collapse. The dynamical regimes studied here, however, are not predicted to undergo collapse. Instead, distinct, ordered structures, appearing after the “implosion”, yield interesting new observables that may be experimentally accessible.}, number={3}, journal={PHYSICS LETTERS A}, author={Tovbis, Alexander and Hoefer, M. A.}, year={2011}, month={Jan}, pages={726–732} }
 @article{hoefer_silva_keller_2010, title={Theory for a dissipative droplet soliton excited by a spin torque nanocontact}, volume={82}, ISSN={["2469-9969"]}, DOI={10.1103/physrevb.82.054432}, abstractNote={A distinct type of solitary wave is predicted to form in spin torque oscillators when the free layer has a sufficiently large perpendicular anisotropy. In this structure, which is a dissipative version of the conservative droplet soliton originally studied in 1977 by Ivanov and Kosevich, spin torque counteracts the damping that would otherwise destroy the mode. Asymptotic methods are used to derive conditions on perpendicular anisotropy strength and applied current under which a dissipative droplet can be nucleated and sustained. Numerical methods are used to confirm the stability of the droplet against various perturbations that are likely in experiments, including tilting of the applied field, nonzero spin torque asymmetry, and nontrivial Oersted fields. Under certain conditions, the droplet experiences a drift instability in which it propagates away from the nanocontact and is then destroyed by damping.}, number={5}, journal={PHYSICAL REVIEW B}, author={Hoefer, M. A. and Silva, T. J. and Keller, Mark W.}, year={2010}, month={Aug} }
 @article{hoefer_ilan_2009, title={Theory of two-dimensional oblique dispersive shock waves in supersonic flow of a superfluid}, volume={80}, ISSN={["1094-1622"]}, DOI={10.1103/physreva.80.061601}, abstractNote={One of the hallmarks of supersonic flows is the formation of shock waves, which are nonlinear disturbances in the fluid’s material and thermodynamic properties. In dissipative media, self-steepening can lead to the formation of viscous shock waves VSWs, which are localized, sharp jumps in the fluid properties. Geometry plays a key role in VSW formation: a two-dimensional 2D supersonic flow when turned through a compression, e.g., by an obstacle, can lead to a VSW. Straight, oblique, and curved detached VSWs can form when the flow is supersonic or transonic, respectively 1. These stationary shock patterns can exhibit stable rich dynamical behavior 2 and have recently found application in the study of granular flows 3.}, number={6}, journal={PHYSICAL REVIEW A}, author={Hoefer, M. A. and Ilan, B.}, year={2009}, month={Dec} }