dorsal/arxiv
View SchemaPainlev\'{e} analysis of the coupled nonlinear Schr\"{o}dinger equation for polarized optical waves in an isotropic medium
| Authors | Q-Han Park, H. J. Shin |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9904009 |
| URL | https://arxiv.org/abs/solv-int/9904009 |
| DOI | 10.1103/PhysRevE.59.2373 |
| Journal | Phys. Rev. E {\bf 59} 2373, 1999 |
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 $\chi^{(3)} $ imposed by these new integrable equations are explained.
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"abstract": "Using the Painlev\\\u0027{e} analysis, we investigate the integrability properties\nof a system of two coupled nonlinear Schr\\\"{o}dinger equations that describe\nthe propagation of orthogonally polarized optical waves in an isotropic medium.\nBesides the well-known integrable vector nonlinear Schr\\\"{o}dinger equation, we\nshow that there exist a new set of equations passing the Painlev\\\u0027{e} test\nwhere the self and cross phase modulational terms are of different magnitude.\nWe introduce the Hirota bilinearization and the B\\\"{a}cklund transformation to\nobtain soliton solutions and prove integrability by making a change of\nvariables. The conditions on the third-order susceptibility tensor $\\chi^{(3)}\n$ imposed by these new integrable equations are explained.",
"arxiv_id": "solv-int/9904009",
"authors": [
"Q-Han Park",
"H. J. Shin"
],
"categories": [
"solv-int",
"nlin.SI"
],
"doi": "10.1103/PhysRevE.59.2373",
"journal_ref": "Phys. Rev. E {\\bf 59} 2373, 1999",
"title": "Painlev\\\u0027{e} analysis of the coupled nonlinear Schr\\\"{o}dinger equation for polarized optical waves in an isotropic medium",
"url": "https://arxiv.org/abs/solv-int/9904009"
},
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