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Conservation Laws in Higher-Order Nonlinear Optical Effects

Jongbae Kim·Q-Han Park·H. J. Shin
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Abstract

Conservation laws of the nonlinear Schrödinger 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 Schrödinger equation. The first few currents and charges are also presented explicitly. Due to the higher-order effects, conservation laws of the nonlinear Schrödinger 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 Schrödinger equation.

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BibTeXRIS

Jongbae Kim, Q-Han Park, H. J. Shin. 1999-04-06. Conservation Laws in Higher-Order Nonlinear Optical Effects. https://doi.org/10.1103/physreve.58.6746

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