Fully nonlinear (2+1)-dimensional displacement shallow water wave equation |
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| Institution: | 1.State Key Laboratory of Structural Analysis of Industrial Equipment, Faculty of Vehicle Engineering and Mechanics, Dalian University of Technology, Dalian 116023, China;2.Transportation Equipments and Ocean Engineering College, Dalian Maritime University, Dalian 116026, China |
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| Abstract: | Recently, a new(2+1)-dimensional displacement shallow water wave equation(2DDSWWE) was constructed by applying the variational principle of analytic mechanics in the Lagrange coordinates. However, the simplification of the nonlinear term related to the incompressibility of the shallow water in the 2DDSWWE is a disadvantage of this approach.Applying the theory of nonlinear continuum mechanics, we add some new nonlinear terms to the 2DDSWWE and construct a new fully nonlinear(2+1)-dimensional displacement shallow water wave equation(FN2DDSWWE). The presented FN2DDSWWE contains all nonlinear terms related to the incompressibility of shallow water. The exact travelling-wave solution of the proposed FN2DDSWWE is also obtained, and the solitary-wave solution can be deduced from the presented travelling-wave solution under a special selection of integral constants. |
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| Keywords: | shallow water system Hamilton variational principle displacement solitary wave |
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