Nonlocal symmetries and explicit solutions of the AKNS system

Qian Miao; Xiangpeng Xin; Yong Chen

doi:10.1016/j.aml.2013.09.002

Nonlocal symmetries and explicit solutions of the AKNS system

Qian Miao, Xiangpeng Xin, Yong Chen

School of Mathematical Sciences

East China Normal University

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

17 Scopus citations

Abstract

In this letter, based on the Lax pair of the Ablowitz-Kaup-Newell-Segur (AKNS) system, the nonlocal symmetry is obtained and successfully localized to a Lie point symmetry by introducing an appropriate auxiliary dependent variable. For the closed prolongation, the construction for the one-dimensional optimal system is presented in detail. Furthermore, using the obtained optimal system, we give the reductions and the explicit analytic interaction solutions between cnoidal waves and solitary waves. For some interesting solutions, the figures are given to show their properties.

Original language	English
Pages (from-to)	7-13
Number of pages	7
Journal	Applied Mathematics Letters
Volume	28
DOIs	https://doi.org/10.1016/j.aml.2013.09.002
State	Published - Feb 2014

Keywords

Auxiliary system
Lie point symmetry
Nonlocal symmetry
Optimal system

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10.1016/j.aml.2013.09.002

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abstract = "In this letter, based on the Lax pair of the Ablowitz-Kaup-Newell-Segur (AKNS) system, the nonlocal symmetry is obtained and successfully localized to a Lie point symmetry by introducing an appropriate auxiliary dependent variable. For the closed prolongation, the construction for the one-dimensional optimal system is presented in detail. Furthermore, using the obtained optimal system, we give the reductions and the explicit analytic interaction solutions between cnoidal waves and solitary waves. For some interesting solutions, the figures are given to show their properties.",

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AU - Miao, Qian

AU - Xin, Xiangpeng

AU - Chen, Yong

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N2 - In this letter, based on the Lax pair of the Ablowitz-Kaup-Newell-Segur (AKNS) system, the nonlocal symmetry is obtained and successfully localized to a Lie point symmetry by introducing an appropriate auxiliary dependent variable. For the closed prolongation, the construction for the one-dimensional optimal system is presented in detail. Furthermore, using the obtained optimal system, we give the reductions and the explicit analytic interaction solutions between cnoidal waves and solitary waves. For some interesting solutions, the figures are given to show their properties.

AB - In this letter, based on the Lax pair of the Ablowitz-Kaup-Newell-Segur (AKNS) system, the nonlocal symmetry is obtained and successfully localized to a Lie point symmetry by introducing an appropriate auxiliary dependent variable. For the closed prolongation, the construction for the one-dimensional optimal system is presented in detail. Furthermore, using the obtained optimal system, we give the reductions and the explicit analytic interaction solutions between cnoidal waves and solitary waves. For some interesting solutions, the figures are given to show their properties.

KW - Auxiliary system

KW - Lie point symmetry

KW - Nonlocal symmetry

KW - Optimal system

UR - https://www.scopus.com/pages/publications/84888351923

U2 - 10.1016/j.aml.2013.09.002

DO - 10.1016/j.aml.2013.09.002

M3 - 文章

AN - SCOPUS:84888351923

SN - 0893-9659

VL - 28

SP - 7

EP - 13

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

ER -

Nonlocal symmetries and explicit solutions of the AKNS system

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Keywords

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