A Truncated Painlevé Expansion and Exact Analytical Solutions for the Nonlinear Schrödinger Equation with Variable Coefficients

Biao Li; Yong Chen

doi:10.1515/zna-2005-11-1202

A Truncated Painlevé Expansion and Exact Analytical Solutions for the Nonlinear Schrödinger Equation with Variable Coefficients

Biao Li, Yong Chen

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

7 Scopus citations

Abstract

By using the truncated Painleve expansion analysis an auto-Backlund transformation is found for the nonlinear Schrödinger equation with varying dispersion, nonlinearity, and gain or absorption. Then, based on the obtained auto-Backlund transformation and symbolic computation, we explore some explicit exact solutions including soliton-like solutions, singular soliton-like solutions, which may be useful to explain the corresponding physical phenomena. Further, the formation and interaction of solitons are simulated by computer. - PACS Nos.: 05.45.Yv, 02.30.Jr, 42.65.Tg.

Original language	English
Pages (from-to)	768-774
Number of pages	7
Journal	Zeitschrift fur Naturforschung - Section A Journal of Physical Sciences
Volume	60
Issue number	11-12
DOIs	https://doi.org/10.1515/zna-2005-11-1202
State	Published - Dec 2005
Externally published	Yes

Keywords

Backlund Transformation
Nonlinear Schrödinger Equation; Solitons
Symbolic Computation
Truncated Painleve Expansion

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10.1515/zna-2005-11-1202

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title = "A Truncated Painlev{\'e} Expansion and Exact Analytical Solutions for the Nonlinear Schr{\"o}dinger Equation with Variable Coefficients",

abstract = "By using the truncated Painleve expansion analysis an auto-Backlund transformation is found for the nonlinear Schr{\"o}dinger equation with varying dispersion, nonlinearity, and gain or absorption. Then, based on the obtained auto-Backlund transformation and symbolic computation, we explore some explicit exact solutions including soliton-like solutions, singular soliton-like solutions, which may be useful to explain the corresponding physical phenomena. Further, the formation and interaction of solitons are simulated by computer. - PACS Nos.: 05.45.Yv, 02.30.Jr, 42.65.Tg.",

keywords = "Backlund Transformation, Nonlinear Schr{\"o}dinger Equation; Solitons, Symbolic Computation, Truncated Painleve Expansion",

author = "Biao Li and Yong Chen",

year = "2005",

month = dec,

doi = "10.1515/zna-2005-11-1202",

language = "英语",

volume = "60",

pages = "768--774",

journal = "Zeitschrift fur Naturforschung - Section A Journal of Physical Sciences",

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TY - JOUR

T1 - A Truncated Painlevé Expansion and Exact Analytical Solutions for the Nonlinear Schrödinger Equation with Variable Coefficients

AU - Li, Biao

AU - Chen, Yong

PY - 2005/12

Y1 - 2005/12

N2 - By using the truncated Painleve expansion analysis an auto-Backlund transformation is found for the nonlinear Schrödinger equation with varying dispersion, nonlinearity, and gain or absorption. Then, based on the obtained auto-Backlund transformation and symbolic computation, we explore some explicit exact solutions including soliton-like solutions, singular soliton-like solutions, which may be useful to explain the corresponding physical phenomena. Further, the formation and interaction of solitons are simulated by computer. - PACS Nos.: 05.45.Yv, 02.30.Jr, 42.65.Tg.

AB - By using the truncated Painleve expansion analysis an auto-Backlund transformation is found for the nonlinear Schrödinger equation with varying dispersion, nonlinearity, and gain or absorption. Then, based on the obtained auto-Backlund transformation and symbolic computation, we explore some explicit exact solutions including soliton-like solutions, singular soliton-like solutions, which may be useful to explain the corresponding physical phenomena. Further, the formation and interaction of solitons are simulated by computer. - PACS Nos.: 05.45.Yv, 02.30.Jr, 42.65.Tg.

KW - Backlund Transformation

KW - Nonlinear Schrödinger Equation; Solitons

KW - Symbolic Computation

KW - Truncated Painleve Expansion

UR - https://www.scopus.com/pages/publications/31544450514

U2 - 10.1515/zna-2005-11-1202

DO - 10.1515/zna-2005-11-1202

M3 - 文章

AN - SCOPUS:31544450514

SN - 0932-0784

VL - 60

SP - 768

EP - 774

JO - Zeitschrift fur Naturforschung - Section A Journal of Physical Sciences

JF - Zeitschrift fur Naturforschung - Section A Journal of Physical Sciences

IS - 11-12

ER -

A Truncated Painlevé Expansion and Exact Analytical Solutions for the Nonlinear Schrödinger Equation with Variable Coefficients

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Keywords

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