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Nonlinear and spectral stability of periodic traveling wave solutions for a nonlinear Schrödinger system. (English) Zbl 1228.76031

Summary: This paper is concerned with nonlinear and spectral stability of periodic traveling wave solutions for a nonlinear Schrödinger type system arising in nonlinear optics. We prove the existence of two smooth curves of periodic solutions depending on conoidal-type functions. In the framework established by M. Grillakis, J. Shatah and W. Strauss, we prove a stability result under perturbations having the same minimal wavelength and zero mean over their fundamental period. By using the so-called Bloch wave decomposition theory, we show spectral stability for a general class of periodic solutions.

MSC:

76B25 Solitary waves for incompressible inviscid fluids
35C07 Traveling wave solutions
35Q55 NLS equations (nonlinear Schrödinger equations)
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