Vahagn Manukian

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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(More)
We consider a known model that describes formation of mussel beds on soft sediments. The model consists of nonlinearly coupled pdes that capture evolution of mussel biomass on the sediment and algae in the water layer overlying the mussel bed. The system accounts for the diffusive spread of mussel, while the diffusion of algae is neglected and at the same(More)
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. Mathematics Subject Classification: 76D08, 34B16, 34B40, 34C37 (Some figures in this article are in colour only in the(More)
For a wide range of parameters, we study travelling waves in a diffusive version of the Holling-Tanner predator-prey model from population dynamics. Fronts are constructed using geometric singular perturbation theory and the theory of rotated vector fields. We focus on the appearance of the fronts in various singular limits. In addition, periodic travelling(More)
Analysis of the intracardiac hemodynamics have been made in 16 patients before and after making prosthetic appliance of the mitral valve EMIKS. The examination of the patients carried out 8.3 +/- 0.4 months after the operation showed that significant improvement of the intracardiac hemodynamics took place in patients with mitral valvular disease after the(More)
For wide range of parameters, we study traveling waves in a diffusive version of the Holling-Tanner predator-prey model from population dynamics. Fronts are constructed using geometric singular perturbation theory and the theory of rotated vector fields. We focus on the appearance of the fronts in various singular limits. In addition, periodic traveling(More)
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 nonsingular 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(More)
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