Painlev\'{e} analysis of the coupled nonlinear Schr\"{o}dinger equation for polarized optical waves in an isotropic medium
solv-int
2009-10-31 v1 Exactly Solvable and Integrable Systems
Abstract
Using the Painlev\'{e} analysis, we investigate the integrability properties of a system of two coupled nonlinear Schr\"{o}dinger equations that describe the propagation of orthogonally polarized optical waves in an isotropic medium. Besides the well-known integrable vector nonlinear Schr\"{o}dinger equation, we show that there exist a new set of equations passing the Painlev\'{e} test where the self and cross phase modulational terms are of different magnitude. We introduce the Hirota bilinearization and the B\"{a}cklund transformation to obtain soliton solutions and prove integrability by making a change of variables. The conditions on the third-order susceptibility tensor imposed by these new integrable equations are explained.
Keywords
Cite
@article{arxiv.solv-int/9904009,
title = {Painlev\'{e} analysis of the coupled nonlinear Schr\"{o}dinger equation for polarized optical waves in an isotropic medium},
author = {Q-Han Park and H. J. Shin},
journal= {arXiv preprint arXiv:solv-int/9904009},
year = {2009}
}