Advances in Differential Equations

Nonlinear travelling waves on complete Riemannian manifolds

Mayukh Mukherjee

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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).

Article information

Source
Adv. Differential Equations Volume 23, Number 1/2 (2018), 65-88.

Dates
First available in Project Euclid: 26 October 2017

Permanent link to this document
https://projecteuclid.org/euclid.ade/1508983360

Subjects
Primary: 35J61: Semilinear elliptic equations 35H20: Subelliptic equations

Citation

Mukherjee, Mayukh. Nonlinear travelling waves on complete Riemannian manifolds. Adv. Differential Equations 23 (2018), no. 1/2, 65--88. https://projecteuclid.org/euclid.ade/1508983360


Export citation