Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
1999-04-06
Phys. Rev. E {\bf 58} 6746, 1998
Nonlinear Sciences
Exactly Solvable and Integrable Systems
Scientific paper
10.1103/PhysRevE.58.6746
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.
Kim Jongbae
Park Q.-Han
Shin Ho-Jeong
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