Radial standing and self-similar waves for the hyperbolic cubic NLS in 2D
Pattern Formation and Solitons
2015-05-27 v1 Mathematical Physics
Analysis of PDEs
math.MP
Abstract
In this note we propose a new set of coordinates to study the hyperbolic or non-elliptic cubic nonlinear Schrodinger equation in two dimensions. Based on these coordinates, we study the existence of bounded and continuous hyperbolically radial standing waves, as well as hyperbolically radial self-similar solutions. Many of the arguments can easily be adapted to more general nonlinearities.
Keywords
Cite
@article{arxiv.1102.2374,
title = {Radial standing and self-similar waves for the hyperbolic cubic NLS in 2D},
author = {P. G. Kevrekidis and A. R. Nahmod and C. Zeng},
journal= {arXiv preprint arXiv:1102.2374},
year = {2015}
}
Comments
19 pages, 1 Figure, to appear in Nonlinearity