January/February 2018 Nonlinear travelling waves on complete Riemannian manifolds
Mayukh Mukherjee
Adv. Differential Equations 23(1/2): 65-88 (January/February 2018). DOI: 10.57262/ade/1508983360

Abstract

We study travelling wave solutions to nonlinear Schrödinger and Klein-Gordon equations on complete Riemannian manifolds, which have a bounded Killing field $X$. For a natural class of power-type nonlinearities, we use standard variational techniques to demonstrate the existence of travelling waves on complete weakly homogeneous manifolds. If the manifolds in question are weakly isotropic, we prove that they have genuine subsonic travelling waves, at least for a non-empty set of parameters. Finally we establish that a slight perturbation of the Killing field $X$ will result in a controlled perturbation of the travelling wave solutions (in appropriate $L^p$-norms).

Citation

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Mayukh Mukherjee. "Nonlinear travelling waves on complete Riemannian manifolds." Adv. Differential Equations 23 (1/2) 65 - 88, January/February 2018. https://doi.org/10.57262/ade/1508983360

Information

Published: January/February 2018
First available in Project Euclid: 26 October 2017

zbMATH: 1384.35028
MathSciNet: MR3717162
Digital Object Identifier: 10.57262/ade/1508983360

Subjects:
Primary: 35H20 , 35J61

Rights: Copyright © 2018 Khayyam Publishing, Inc.

Vol.23 • No. 1/2 • January/February 2018
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