@article{manukian_schecter_2021, title={MORE TRAVELING WAVES IN THE HOLLING-TANNER MODEL WITH WEAK DIFFUSION}, ISSN={["1553-524X"]}, DOI={10.3934/dcdsb.2021256}, abstractNote={We identify two new traveling waves of the Holling-Tanner model with weak diffusion. One connects two constant states; at one of them, the model is undefined. The other connects a constant state to a periodic wave train. We exploit the multi-scale structure of the Holling-Tanner model in the weak diffusion limit. Our analysis uses geometric singular perturbation theory, compactification and the blow-up method.}, journal={DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B}, author={Manukian, Vahagn and Schecter, Stephen}, year={2021}, month={Oct} }
 @article{manukian_costanzino_jones_sandstede_2009, title={Existence of Multi-Pulses of the Regularized Short-Pulse and Ostrovsky Equations}, volume={21}, ISSN={["1572-9222"]}, DOI={10.1007/s10884-009-9147-4}, abstractNote={The existence of multi-pulse solutions near orbit-flip bifurcations of a primary single-humped pulse is shown in reversible, conservative, singularly perturbed vector fields. Similar to the non-singular case, the sign of a geometric condition that involves the first integral decides whether multi-pulses exist or not. The proof utilizes a combination of geometric singular perturbation theory and Lyapunov–Schmidt reduction through Lin’s method. The motivation for considering orbit flips in singularly perturbed systems comes from the regularized short-pulse equation and the Ostrovsky equation, which both fit into this framework and are shown here to support multi-pulses.}, number={4}, journal={JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS}, author={Manukian, Vahagn and Costanzino, Nicola and Jones, Christopher K. R. T. and Sandstede, Bjoern}, year={2009}, month={Dec}, pages={607–622} }
 @article{costanzino_manukian_jones_2009, title={SOLITARY WAVES OF THE REGULARIZED SHORT PULSE AND OSTROVSKY EQUATIONS}, volume={41}, ISSN={["1095-7154"]}, DOI={10.1137/080734327}, abstractNote={We derive a model for the propagation of short pulses in nonlinear media. The model is a higher-order regularization of the short-pulse equation (SPE). The regularization term arises as the next term in the expansion of the susceptibility in derivation of the SPE. Without the regularization term there do not exist traveling pulses in the class of piecewise smooth functions with one discontinuity. However, when the regularization term is added, we show, for a particular parameter regime, that the equation supports smooth traveling waves which have structure similar to solitary waves of the modified Korteweg–deVries equation. The existence of such traveling pulses is proved via the Fenichel theory for singularly perturbed systems and a Melnikov-type transversality calculation. Corresponding statements for the Ostrovsky equations are also included.}, number={5}, journal={SIAM JOURNAL ON MATHEMATICAL ANALYSIS}, author={Costanzino, Nicola and Manukian, Vahagn and Jones, Christopher K. R. T.}, year={2009}, pages={2088–2106} }
 @article{manukian_schecter_2009, title={Travelling waves for a thin liquid film with surfactant on an inclined plane}, volume={22}, ISSN={["1361-6544"]}, DOI={10.1088/0951-7715/22/1/006}, abstractNote={We show the existence of travelling wave solutions for a lubrication model of surfactant-driven flow of a thin liquid film down an inclined plane, in various parameter regimes. Our arguments use geometric singular perturbation theory.}, number={1}, journal={NONLINEARITY}, author={Manukian, Vahagn and Schecter, Stephen}, year={2009}, month={Jan}, pages={85–122} }