Fully nonlinear (2+1)-dimensional displacement shallow water wave equation  

作　　者：吴锋 姚征 钟万勰 

机构地区：[1]State Key Laboratory of Structural Analysis of Industrial Equipment, Faculty of Vehicle Engineering and Mechanics,Dalian University of Technology [2]Transportation Equipments and Ocean Engineering College, Dalian Maritime University

出　　处：《Chinese Physics B》2017年第5期253-258,共6页中国物理B（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(Grant Nos.11272076 and 51609034);China Postdoctoral Science Foundation(Grant No.2016M590219)

摘　　要：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.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.

关 键 词：shallow travelling solitary constants variational coordinates analytic exact disadvantage Boussinesq 

分 类 号：O175[理学—数学]