The \(\varvec{(2+1)}\) -dimensional Konopelchenko–Dubrovsky equation: nonlocal symmetries and interaction solutions

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• 作者：Bo Ren ; Xue-Ping Cheng ; Ji Lin
• 关键词：Konopelchenko–Dubrovsky equation ; Nonlocal symmetries ; Symmetry reduction
• 刊名：Nonlinear Dynamics
• 出版年：2016
• 出版时间：November 2016
• 年：2016
• 卷：86
• 期：3
• 页码：1855-1862
• 全文大小：3,003 KB
• 刊物类别：Engineering
• 刊物主题：Vibration, Dynamical Systems and Control
  Mechanics
  Mechanical Engineering
  Automotive and Aerospace Engineering and Traffic
  
• 出版者：Springer Netherlands
• ISSN：1573-269X
• 卷排序：86

文摘

The nonlocal symmetries for the \((2+1)\)-dimensional Konopelchenko–Dubrovsky equation are obtained with the truncated Painlevé method and the Möbious (conformal) invariant form. The nonlocal symmetries are localized to the Lie point symmetries by introducing auxiliary dependent variables. The finite symmetry transformations are obtained by solving the initial value problem of the prolonged systems. The multi-solitary wave solution is presented with the finite symmetry transformations of a trivial solution. In the meanwhile, symmetry reductions in the enlarged systems are studied by the Lie point symmetry approach. Many explicit interaction solutions between solitons and cnoidal periodic waves are discussed both in analytical and in graphical ways.