The homoclinic solutions problem of the Davey-Stewartson ( DS) Equations were studied. By using the Hirota's bilinear method, the homoclinic orbits of the Davey-Stewartson Equations were obtained through the depen...The homoclinic solutions problem of the Davey-Stewartson ( DS) Equations were studied. By using the Hirota's bilinear method, the homoclinic orbits of the Davey-Stewartson Equations were obtained through the dependent variable transformation. The homoclinic orbits of the Davey-Stewartson Equations were discussed.展开更多
Chaos is closely associated with homoclinic orbits in deterministic nonlinear dynamics. In this paper, analytic expressions of homoclinic orbits for some （2＋1）- dimensional nonlinear Schrodinger-like equations are ...Chaos is closely associated with homoclinic orbits in deterministic nonlinear dynamics. In this paper, analytic expressions of homoclinic orbits for some （2＋1）- dimensional nonlinear Schrodinger-like equations are constructed based on Hirota＇s bilinear method, including long wave-short wave resonance interaction equation, generalization of the Zakharov equation, Mel＇nikov equation, and g-Schrodinger equation are constructed based on Hirota＇s bilinear method.展开更多
The extended homoclinic test function method is a kind of classic, efficient and well-developed method to solve nonlinear evolution equations. In this paper, with the help of this approach, we obtain new exact solutio...The extended homoclinic test function method is a kind of classic, efficient and well-developed method to solve nonlinear evolution equations. In this paper, with the help of this approach, we obtain new exact solutions （including kinky periodic solitary-wave solutions, periodic soliton solutions, and cross kink-wave solutions） for the new （2＋1）-dimensional KdV equation. These results enrich the variety of the dynamics of higher-dimensionai nonlinear wave field.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
文摘The homoclinic solutions problem of the Davey-Stewartson ( DS) Equations were studied. By using the Hirota's bilinear method, the homoclinic orbits of the Davey-Stewartson Equations were obtained through the dependent variable transformation. The homoclinic orbits of the Davey-Stewartson Equations were discussed.
基金the National Natural Science Foundation of China(No.10501040)
文摘Chaos is closely associated with homoclinic orbits in deterministic nonlinear dynamics. In this paper, analytic expressions of homoclinic orbits for some （2＋1）- dimensional nonlinear Schrodinger-like equations are constructed based on Hirota＇s bilinear method, including long wave-short wave resonance interaction equation, generalization of the Zakharov equation, Mel＇nikov equation, and g-Schrodinger equation are constructed based on Hirota＇s bilinear method.
基金Supported by the Natural Science Foundation of China under Grant Nos.10361007,10661002Yunnan Natural Science Foundation under Grant No.2006A0082M
文摘The extended homoclinic test function method is a kind of classic, efficient and well-developed method to solve nonlinear evolution equations. In this paper, with the help of this approach, we obtain new exact solutions （including kinky periodic solitary-wave solutions, periodic soliton solutions, and cross kink-wave solutions） for the new （2＋1）-dimensional KdV equation. These results enrich the variety of the dynamics of higher-dimensionai nonlinear wave field.
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.
