Nonlocal symmetries and similarity reductions for Korteweg-de Vries-negative-order Korteweg-de Vries equation

doi:10.1088/1674-1056/ab6dca

中国物理B ›› 2020, Vol. 29 ›› Issue (4): 40201-040201.doi: 10.1088/1674-1056/ab6dca

• GENERAL • 下一篇

Nonlocal symmetries and similarity reductions for Korteweg-de Vries-negative-order Korteweg-de Vries equation

Heng-Chun Hu(胡恒春), Fei-Yan Liu(刘飞艳)

College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China

收稿日期:2019-12-05 修回日期:2020-01-21 出版日期:2020-04-05 发布日期:2020-04-05
通讯作者: Heng-Chun Hu E-mail:hhengchun@163.com
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 11471215).

Nonlocal symmetries and similarity reductions for Korteweg-de Vries-negative-order Korteweg-de Vries equation

Heng-Chun Hu(胡恒春), Fei-Yan Liu(刘飞艳)

College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China

Received:2019-12-05 Revised:2020-01-21 Online:2020-04-05 Published:2020-04-05
Contact: Heng-Chun Hu E-mail:hhengchun@163.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 11471215).

摘要/Abstract

摘要： The nonlocal symmetries are derived for the Korteweg-de Vries-negative-order Korteweg-de Vries equation from the Painlevé truncation method. The nonlocal symmetries are localized to the classical Lie point symmetries for the enlarged system by introducing new dependent variables. The corresponding similarity reduction equations are obtained with different constant selections. Many explicit solutions for the integrable equation can be presented from the similarity reduction.

关键词: nonlocal symmetry, symmetry reduction, Lie point symmetry, KdV-nKdV equation

Abstract: The nonlocal symmetries are derived for the Korteweg-de Vries-negative-order Korteweg-de Vries equation from the Painlevé truncation method. The nonlocal symmetries are localized to the classical Lie point symmetries for the enlarged system by introducing new dependent variables. The corresponding similarity reduction equations are obtained with different constant selections. Many explicit solutions for the integrable equation can be presented from the similarity reduction.

Key words: nonlocal symmetry, symmetry reduction, Lie point symmetry, KdV-nKdV equation

中图分类号: (Integrable systems)

02.30.Ik

04.20.Jb (Exact solutions) 05.45.Yv (Solitons)

胡恒春, 刘飞艳. Nonlocal symmetries and similarity reductions for Korteweg-de Vries-negative-order Korteweg-de Vries equation[J]. 中国物理B, 2020, 29(4): 40201-040201.

Heng-Chun Hu(胡恒春), Fei-Yan Liu(刘飞艳). Nonlocal symmetries and similarity reductions for Korteweg-de Vries-negative-order Korteweg-de Vries equation[J]. Chin. Phys. B, 2020, 29(4): 40201-040201.

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Nonlocal symmetries and similarity reductions for Korteweg-de Vries-negative-order Korteweg-de Vries equation

Nonlocal symmetries and similarity reductions for Korteweg-de Vries-negative-order Korteweg-de Vries equation

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