Singularity analysis, balance equations and soliton solution of the nonlocal complex Ginzburg-Landau equation

A. Ankiewicz; N. N. Akhmediev; P. Winternitz

doi:10.1023/a:1004533704679

Singularity analysis, balance equations and soliton solution of the nonlocal complex Ginzburg-Landau equation

A. Ankiewicz^*, N. N. Akhmediev, P. Winternitz

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

The modified complex Ginzburg-Landau equation (mCGLE) which includes a delayed response term in the integral form is analysed. In particular, a singularity analysis of mCGLE is presented. It is shown that this equation fails to pass the Painlevé test when the non-conservative terms are nonzero. Nevertheless, exact solutions to this equation do exist. Stationary solutions can be treated using the 'segment balance' method which is an extension of conservation laws to non-conservative systems. This method is used to derive an exact soliton solution of mCGLE.

Original language	English
Pages (from-to)	11-24
Number of pages	14
Journal	Journal of Engineering Mathematics
Volume	36
Issue number	1-2
DOIs	https://doi.org/10.1023/a:1004533704679
Publication status	Published - 1999

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title = "Singularity analysis, balance equations and soliton solution of the nonlocal complex Ginzburg-Landau equation",

abstract = "The modified complex Ginzburg-Landau equation (mCGLE) which includes a delayed response term in the integral form is analysed. In particular, a singularity analysis of mCGLE is presented. It is shown that this equation fails to pass the Painlev{\'e} test when the non-conservative terms are nonzero. Nevertheless, exact solutions to this equation do exist. Stationary solutions can be treated using the 'segment balance' method which is an extension of conservation laws to non-conservative systems. This method is used to derive an exact soliton solution of mCGLE.",

keywords = "Complex ginzburg-landau equation, Integrability, Singularity analysis, Solitons",

author = "A. Ankiewicz and Akhmediev, {N. N.} and P. Winternitz",

year = "1999",

doi = "10.1023/a:1004533704679",

language = "English",

volume = "36",

pages = "11--24",

journal = "Journal of Engineering Mathematics",

issn = "0022-0833",

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T1 - Singularity analysis, balance equations and soliton solution of the nonlocal complex Ginzburg-Landau equation

AU - Ankiewicz, A.

AU - Akhmediev, N. N.

AU - Winternitz, P.

PY - 1999

Y1 - 1999

N2 - The modified complex Ginzburg-Landau equation (mCGLE) which includes a delayed response term in the integral form is analysed. In particular, a singularity analysis of mCGLE is presented. It is shown that this equation fails to pass the Painlevé test when the non-conservative terms are nonzero. Nevertheless, exact solutions to this equation do exist. Stationary solutions can be treated using the 'segment balance' method which is an extension of conservation laws to non-conservative systems. This method is used to derive an exact soliton solution of mCGLE.

AB - The modified complex Ginzburg-Landau equation (mCGLE) which includes a delayed response term in the integral form is analysed. In particular, a singularity analysis of mCGLE is presented. It is shown that this equation fails to pass the Painlevé test when the non-conservative terms are nonzero. Nevertheless, exact solutions to this equation do exist. Stationary solutions can be treated using the 'segment balance' method which is an extension of conservation laws to non-conservative systems. This method is used to derive an exact soliton solution of mCGLE.

KW - Complex ginzburg-landau equation

KW - Integrability

KW - Singularity analysis

KW - Solitons

UR - http://www.scopus.com/inward/record.url?scp=0033390927&partnerID=8YFLogxK

U2 - 10.1023/a:1004533704679

DO - 10.1023/a:1004533704679

M3 - Article

SN - 0022-0833

VL - 36

SP - 11

EP - 24

JO - Journal of Engineering Mathematics

JF - Journal of Engineering Mathematics

IS - 1-2

ER -

Singularity analysis, balance equations and soliton solution of the nonlocal complex Ginzburg-Landau equation

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