In this paper,the bidirectional SK-Ramani equation is investigated by means of the extended homoclinic test approach and Riemann theta function method,respectively.Based on the Hirota bilinear method,exact solutions i...In this paper,the bidirectional SK-Ramani equation is investigated by means of the extended homoclinic test approach and Riemann theta function method,respectively.Based on the Hirota bilinear method,exact solutions including one-soliton wave solution are obtained by using the extended homoclinic approach and one-periodic wave solution is constructed by using the Riemann theta function method.A limiting procedure is presented to analyze in detail the relations between the one periodic wave solution and one-soliton solution.展开更多
We investigate the Lax equation that can be employed to describe motions of long waves in shallow water under gravity.A nonlocal symmetry of this equation is given and used to find exact solutions and derive lower int...We investigate the Lax equation that can be employed to describe motions of long waves in shallow water under gravity.A nonlocal symmetry of this equation is given and used to find exact solutions and derive lower integrable models from higher ones.It is interesting that this nonlocal symmetry links with its corresponding Riccati-type pseudopotential.By introducing suitable and simple auxiliary dependent variables,the nonlocal symmetry is localized and used to generate new solutions from trivial solutions.Meanwhile,this equation is reduced to an ordinary differential equation by means of this nonlocal symmetry and some local symmetries.展开更多
文摘In this paper,the bidirectional SK-Ramani equation is investigated by means of the extended homoclinic test approach and Riemann theta function method,respectively.Based on the Hirota bilinear method,exact solutions including one-soliton wave solution are obtained by using the extended homoclinic approach and one-periodic wave solution is constructed by using the Riemann theta function method.A limiting procedure is presented to analyze in detail the relations between the one periodic wave solution and one-soliton solution.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11275072,11075055the Innovative Research Team Program of the National Natural Science Foundation of China(No 61021004)+1 种基金Shanghai Leading Academic Discipline Project(No B412)the National High-Technology Research and Development Program(No 2011AA010101).
文摘We investigate the Lax equation that can be employed to describe motions of long waves in shallow water under gravity.A nonlocal symmetry of this equation is given and used to find exact solutions and derive lower integrable models from higher ones.It is interesting that this nonlocal symmetry links with its corresponding Riccati-type pseudopotential.By introducing suitable and simple auxiliary dependent variables,the nonlocal symmetry is localized and used to generate new solutions from trivial solutions.Meanwhile,this equation is reduced to an ordinary differential equation by means of this nonlocal symmetry and some local symmetries.
