Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
1999-04-06
Phys. Rev. E {\bf 59} 2373, 1999
Nonlinear Sciences
Exactly Solvable and Integrable Systems
Scientific paper
10.1103/PhysRevE.59.2373
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 $\chi^{(3)} $ imposed by these new integrable equations are explained.
Park Q.-Han
Shin Ho-Jeong
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