### Abstract

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 language | English |
---|---|

Pages (from-to) | 6746-6751 |

Number of pages | 6 |

Journal | Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics |

Volume | 58 |

Issue number | 5 B |

Publication status | Published - 1998 Nov 1 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Mathematical Physics
- Physics and Astronomy(all)
- Condensed Matter Physics
- Statistical and Nonlinear Physics

### Cite this

*Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*,

*58*(5 B), 6746-6751.

**Conservation laws in higher-order nonlinear Schrödinger equations.** / Kim, Jongbae; Park, Q Han; Shin, H. J.

Research output: Contribution to journal › Article

*Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*, vol. 58, no. 5 B, pp. 6746-6751.

}

TY - JOUR

T1 - Conservation laws in higher-order nonlinear Schrödinger equations

AU - Kim, Jongbae

AU - Park, Q Han

AU - Shin, H. J.

PY - 1998/11/1

Y1 - 1998/11/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0032209594&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032209594&partnerID=8YFLogxK

M3 - Article

VL - 58

SP - 6746

EP - 6751

JO - Physical Review E

JF - Physical Review E

SN - 2470-0045

IS - 5 B

ER -