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Exact Solitary-wave Solutions and Periodic Wave Solutions for Generalized Modified Boussinesq Equation and the Effect of Wave Velocity on Wave Shape
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作者 Wei-guo Zhang Shao-wei Li +1 位作者 Wei-zhong Tian Lu Zhang 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2008年第4期691-705,共15页
By means of the undetermined assumption method, we obtain some new exact solitary-wave solutions with hyperbolic secant function fractional form and periodic wave solutions with cosine function form for the generalize... By means of the undetermined assumption method, we obtain some new exact solitary-wave solutions with hyperbolic secant function fractional form and periodic wave solutions with cosine function form for the generalized modified Boussinesq equation. We also discuss the boundedness of these solutions. More over, we study the correlative characteristic of the solitary-wave solutions and the periodic wave solutions along with the travelling wave velocity's variation. 展开更多
关键词 Generalized modified boussinesq equation exact solitary-wave solution periodic wave solution
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CTE Solvability, Nonlocal Symmetry and Explicit Solutions of Modified Boussinesq System 被引量:4
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作者 任博 程雪苹 《Communications in Theoretical Physics》 SCIE CAS CSCD 2016年第7期84-92,共9页
A consistent tanh expansion(CTE) method is used to study the modified Boussinesq equation. It i proved that the modified Boussinesq equation is CTE solvable. The soliton-cnoidal periodic wave is explicitly given by a ... A consistent tanh expansion(CTE) method is used to study the modified Boussinesq equation. It i proved that the modified Boussinesq equation is CTE solvable. The soliton-cnoidal periodic wave is explicitly given by a nonanto-BT theorem. Furthermore, the nonlocal symmetry for the modified Boussinesq equation is obtained by th Painlev′e analysis. The nonlocal symmetry is localized to the Lie point symmetry by introducing one auxiliary dependen variable. The finite symmetry transformation related with the nonlocal symemtry is obtained by solving the initia value problem of the prolonged systems. Thanks to the localization process, many interaction solutions among soliton and other complicated waves are computed through similarity reductions. Some special concrete soliton-cnoidal wav interaction behaviors are studied both in analytical and graphical ways. 展开更多
关键词 modified boussinesq equation CTE method nonlocal symmetry symmetry reduction
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