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2016•Journal of the Association of Arab Universities for Basic and Applied SciencesOpen access

Nonlocal symmetries and interaction solutions for the KdV-type equation

Hengchun Hu, Yujuan Li

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Abstract

The nonlocal symmetries for the special equation, which is called KdV-type equation, are obtained by means of the truncated Painlevé method. The nonlocal symmetries can be localized to the Lie point symmetries by introducing auxiliary dependent variables and the corresponding finite symmetry transformations are computed directly. The KdV-type equation is also proved to be consistent tanh expansion solvable. New exact interaction excitations such as soliton–cnoidal wave solutions are given out analytically and graphically.

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The nonlocal symmetries for the special equation, which is called KdV-type equation, are obtained by means of the truncated Painlevé method. The nonlocal symmetries can be localized to the Lie point symmetries by introducing auxiliary dependent variables and the corresponding finite symmetry transformations are computed directly. The KdV-type equation is also proved to be consistent tanh expansion solvable. New exact interaction excitations such as soliton–cnoidal wave solutions are given out analytically and graphically.

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Available abstract

The nonlocal symmetries for the special equation, which is called KdV-type equation, are obtained by means of the truncated Painlevé method. The nonlocal symmetries can be localized to the Lie point symmetries by introducing auxiliary dependent variables and the corresponding finite symmetry transformations are computed directly. The KdV-type equation is also proved to be consistent tanh expansion solvable. New exact interaction excitations such as soliton–cnoidal wave solutions are given out analytically and graphically.

Key concepts: Korteweg–de Vries equation, Homogeneous space, Type (biology), Symmetry (geometry), Mathematics, Soliton, Mathematical physics, Mathematical analysis

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