Residual symmetries of the modified Korteweg-de Vries equation and its localization

• Authors: Ping Liu , Biao Li , Jian-Rong Yang
• Languages of publication: EN

Abstracts

EN

The residual symmetries of the famous modified Korteweg-de Vries (mKdV) equation are researched in this paper. The initial problem on the residual symmetry of the mKdV equation is researched. The residual symmetries for the mKdV equation are proved to be nonlocal and the nonlocal residual symmetries are extended to the local Lie point symmetries by means of enlarging the mKdV equations. One-parameter invariant subgroups and the invariant solutions for the extended system are listed. Eight types of similarity solutions and the reduction equations are demonstrated. It is noted that we researched the twofold residual symmetries by means of taking the mKdV equation as an example. Similarity solutions and the reduction equations are demonstrated for the extended mKdV equations related to the twofold residual symmetries.

Keywords

EN

residual symmetries; modified Korteweg-de Vries equation; localization; nonlocal symmetries

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2014
• Volume: 12
• Issue: 8
• Pages: 541-553

Dates

published

1 - 8 - 2014

online

20 - 7 - 2014

Contributors

author

Ping Liu

author

Biao Li

• Faculty of Science, Ningbo University, Ningbo, 315211, China

author

Jian-Rong Yang

• Department of Physics and Electronics, Shangrao Normal University, Shangrao, 334001, China

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Identifiers

DOI

10.2478/s11534-014-0488-1