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Traveling wave solutions in optical metamaterials equation. (English) Zbl 1393.35215

Summary: This paper is concerned with the traveling wave solutions in a optical metamaterials, which is governed by a generalized nonlinear Schrödinger equation. Applying the dynamical system theory of singular traveling wave systems, the existence of some traveling wave solutions for this equation are established. Moreover, the exact representation of solitary wave solutions, kink and anti-kink wave solutions, peakons, compactons and periodic cusp solutions are obtained accordingly.

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
35B32 Bifurcations in context of PDEs
35G20 Nonlinear higher-order PDEs
37C29 Homoclinic and heteroclinic orbits for dynamical systems
35C07 Traveling wave solutions
35C08 Soliton solutions
78A40 Waves and radiation in optics and electromagnetic theory
78A60 Lasers, masers, optical bistability, nonlinear optics
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References:

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