Conservation laws in higher-order nonlinear Schrödinger equations

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

Research output: Contribution to journalArticle

48 Citations (Scopus)

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 languageEnglish
Pages (from-to)6746-6751
Number of pages6
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume58
Issue number5 B
Publication statusPublished - 1998 Nov 1
Externally publishedYes

Fingerprint

Higher order equation
conservation laws
Conservation Laws
nonlinear equations
Nonlinear Equations
Higher Order
Charge
Conserved Quantity
group theory
Group Theory
Imply
Term

ASJC Scopus subject areas

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

Cite this

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

In: Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Vol. 58, No. 5 B, 01.11.1998, p. 6746-6751.

Research output: Contribution to journalArticle

@article{aff2a1eeaa8e45b88e4e70e802165808,
title = "Conservation laws in higher-order nonlinear Schr{\"o}dinger equations",
abstract = "Conservation laws of the nonlinear Schr{\"o}dinger 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 Schr{\"o}dinger equation. The first few currents and associated charges are also presented explicitly. Due to the higher-order effects, the 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 case of the higher-order nonlinear Schr{\"o}dinger equation.",
author = "Jongbae Kim and Park, {Q Han} and Shin, {H. J.}",
year = "1998",
month = "11",
day = "1",
language = "English",
volume = "58",
pages = "6746--6751",
journal = "Physical Review E",
issn = "2470-0045",
publisher = "American Physical Society",
number = "5 B",

}

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 -