Conservation laws in higher-order nonlinear Schrödinger equations

Jongbae Kim, Q. Han Park, H. J. Shin

Research output: Contribution to journalArticlepeer-review

60 Citations (Scopus)


Conservation laws of the nonlinear Schrödinger equation are studied in the presence of higher-order optical effects including the third-order dispersion and the self-steepening. In a context of group theory, we derive general expressions for infinitely many conserved currents and charges of a coupled higher-order nonlinear Schrödinger equation. The first few currents and associated charges are also presented explicitly. Due to the higher-order effects, the 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 case of the higher-order nonlinear Schrödinger equation.

Original languageEnglish
Pages (from-to)6746-6751
Number of pages6
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Issue number5
Publication statusPublished - 1998
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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