Some new structures and interactions of solitons for the （2＋1）-dimensional Nizhnik-Novikov-Veselov equation are revealed with the help of the idea of the bilinear method and variable separation approach. The soluti...Some new structures and interactions of solitons for the （2＋1）-dimensional Nizhnik-Novikov-Veselov equation are revealed with the help of the idea of the bilinear method and variable separation approach. The solutions to describe the interactions between two dromions, between a line soliton and a y-periodic soliton, and between two y-periodic solitons are included in our results. Detailed behaviors of interaction are illustrated both analytically and in graphically. Our analysis shows that the interaction properties between two solitons are related to the form of interaction constant. The form of interaction constant and the dispersion relationship are related to the form of the seed solution （u0, v0, w0 ） in Backlund transformation.展开更多
The Gardner equation with a variable-coefficient from fluid dynamics and plasma physics is investigated. Different kinds of solutions including breather-type soliton and two soliton solutions are obtained using biline...The Gardner equation with a variable-coefficient from fluid dynamics and plasma physics is investigated. Different kinds of solutions including breather-type soliton and two soliton solutions are obtained using bilinear method and extended homoclinic test approach. The proposed method can also be applied to solve other types of higher dimensional integrable and non-integrable systems.展开更多
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
基金The project supported by the State Key Laboratory of 0il/Gas Reservoir Geology and Exploitation ＂PLN0402＂The authors would like to thank Prof.Sen-Yue Lou for helpful discussions.
文摘Some new structures and interactions of solitons for the （2＋1）-dimensional Nizhnik-Novikov-Veselov equation are revealed with the help of the idea of the bilinear method and variable separation approach. The solutions to describe the interactions between two dromions, between a line soliton and a y-periodic soliton, and between two y-periodic solitons are included in our results. Detailed behaviors of interaction are illustrated both analytically and in graphically. Our analysis shows that the interaction properties between two solitons are related to the form of interaction constant. The form of interaction constant and the dispersion relationship are related to the form of the seed solution （u0, v0, w0 ） in Backlund transformation.
文摘The Gardner equation with a variable-coefficient from fluid dynamics and plasma physics is investigated. Different kinds of solutions including breather-type soliton and two soliton solutions are obtained using bilinear method and extended homoclinic test approach. The proposed method can also be applied to solve other types of higher dimensional integrable and non-integrable systems.
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.
