dorsal/arxiv
View SchemaConservation Laws in Higher-Order Nonlinear Optical Effects
| Authors | Jongbae Kim, Q-Han Park, H. J. Shin |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9904008 |
| URL | https://arxiv.org/abs/solv-int/9904008 |
| DOI | 10.1103/PhysRevE.58.6746 |
| Journal | Phys. Rev. E {\bf 58} 6746, 1998 |
Abstract
Conservation laws of the nonlinear Schr\"{o}dinger equation are studied in the presence of higher-order nonlinear optical effects including the third-order dispersion and the self-steepening. In a context of group theory, we derive a general expression for infinitely many conserved currents and charges of the coupled higher-order nonlinear Schr\"{o}dinger equation. The first few currents and charges are also presented explicitly. Due to the higher-order effects, conservation laws of the nonlinear Schr\"{o}dinger equation are violated in general. The differences between the types of the conserved currents for the Hirota and the Sasa-Satsuma equations imply that the higher-order terms determine the inherent types of conserved quantities for each integrable cases of the higher-order nonlinear Schr\"{o}dinger equation.
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"abstract": "Conservation laws of the nonlinear Schr\\\"{o}dinger equation are studied in\nthe presence of higher-order nonlinear optical effects including the\nthird-order dispersion and the self-steepening. In a context of group theory,\nwe derive a general expression for infinitely many conserved currents and\ncharges of the coupled higher-order nonlinear Schr\\\"{o}dinger equation. The\nfirst few currents and charges are also presented explicitly. Due to the\nhigher-order effects, conservation laws of the nonlinear Schr\\\"{o}dinger\nequation are violated in general. The differences between the types of the\nconserved currents for the Hirota and the Sasa-Satsuma equations imply that the\nhigher-order terms determine the inherent types of conserved quantities for\neach integrable cases of the higher-order nonlinear Schr\\\"{o}dinger equation.",
"arxiv_id": "solv-int/9904008",
"authors": [
"Jongbae Kim",
"Q-Han Park",
"H. J. Shin"
],
"categories": [
"solv-int",
"nlin.SI"
],
"doi": "10.1103/PhysRevE.58.6746",
"journal_ref": "Phys. Rev. E {\\bf 58} 6746, 1998",
"title": "Conservation Laws in Higher-Order Nonlinear Optical Effects",
"url": "https://arxiv.org/abs/solv-int/9904008"
},
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