PT-Symmetric Extension of the Korteweg-de Vries Equation
Mathematical Physics
2011-07-19 v1 High Energy Physics - Theory
Dynamical Systems
math.MP
Abstract
The Korteweg-de Vries equation u_t+uu_x+u_{xxx}=0 is PT symmetric (invariant under space-time reflection). Therefore, it can be generalized and extended into the complex domain in such a way as to preserve the PT symmetry. The result is the family of complex nonlinear wave equations u_t-iu(i u_x)^epsilon+u_{xxx}=0, where epsilon is real. The features of these equations are discussed. Special attention is given to the epsilon=3 equation, for which conservation laws are derived and solitary waves are investigated.
Keywords
Cite
@article{arxiv.math-ph/0610003,
title = {PT-Symmetric Extension of the Korteweg-de Vries Equation},
author = {Carl M. Bender and Dorje C. Brody and Junhua Chen and Elisabetta Furlan},
journal= {arXiv preprint arXiv:math-ph/0610003},
year = {2011}
}
Comments
9 pages, 6 figures