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July 2010 Stability and bifurcation of periodic travelling waves in a derivative non-linear Schrödinger equation
Kouya Imamura
Hiroshima Math. J. 40(2): 185-203 (July 2010). DOI: 10.32917/hmj/1280754420

Abstract

We study periodic travelling wave solutions of a derivative non-linear Schrödinger equation and show the existence of infinitely many families of semi-trivial solutions (Theorem 2). Each of the families constitutes a branch of travelling waves corresponding to a non-zero integer called the winding number. A sufficient condition for the orbital stability of travelling waves on the branches with positive winding number is given in terms of the wave speed and winding number of the solution (Theorem 3). Bifurcation points are found on each semi-trivial branch of travelling wave solutions (Theorem 4), and the qualitative, and approximately quantitative, orbitshapes of the bifurcated solutions are given. The stability of the semi-trivial solutions under subharmonic perturbations is studied in Theorem 6, and subharmonic bifurcations are established in Theorem 7.

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Kouya Imamura. "Stability and bifurcation of periodic travelling waves in a derivative non-linear Schrödinger equation." Hiroshima Math. J. 40 (2) 185 - 203, July 2010. https://doi.org/10.32917/hmj/1280754420

Information

Published: July 2010
First available in Project Euclid: 2 August 2010

zbMATH: 1227.35121
MathSciNet: MR2680655
Digital Object Identifier: 10.32917/hmj/1280754420

Subjects:
Primary: 35A15, 35B35
Secondary: 35Q55

Rights: Copyright © 2010 Hiroshima University, Mathematics Program

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Vol.40 • No. 2 • July 2010
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