In this paper, we derive the bilinear form for a variable-coefficient Kadomtsev Petviashvili-typed equation. Based on the bilinear form, we obtain the Wronskian determinant solution, which is proved to be indeed an ex...In this paper, we derive the bilinear form for a variable-coefficient Kadomtsev Petviashvili-typed equation. Based on the bilinear form, we obtain the Wronskian determinant solution, which is proved to be indeed an exact solution of this equation through the Wronskian technique. In addition, we testify that this equation can be reduced to a Jacobi identity by considering its solution as a Grammian determinant by means of Pfaffian derivative formulae.展开更多
A spherical Kadomtsev-Petviashvili （SKP） equation for dust acoustic or ion-acoustic waves is studied. Similarity reductions of the SKP equation are obtained with the one-parameter （ε） Lie group of infinitesimal t...A spherical Kadomtsev-Petviashvili （SKP） equation for dust acoustic or ion-acoustic waves is studied. Similarity reductions of the SKP equation are obtained with the one-parameter （ε） Lie group of infinitesimal transformations and Clarkson-Kruskal direct method, The SKP equation is also solved with a generalized tanh function method.展开更多
基金The project supported by the Key Project of the Ministry of Education under Grant No.106033the Specialized Research Fund for the Doctoral Program of Higher Education under Grant No.20060006024+2 种基金National Natural Science Foundation of China under Grant Nos.60372095 and 60772023the Open Fund of the State Key Laboratory of Software Development Environment under Grant No.SKLSDE07-001Beijing University of Aeronautics and Astronautics,and the National Basic Research Program of China(973 Program)under Grant No.2005CB321901
文摘In this paper, we derive the bilinear form for a variable-coefficient Kadomtsev Petviashvili-typed equation. Based on the bilinear form, we obtain the Wronskian determinant solution, which is proved to be indeed an exact solution of this equation through the Wronskian technique. In addition, we testify that this equation can be reduced to a Jacobi identity by considering its solution as a Grammian determinant by means of Pfaffian derivative formulae.
基金The project supported by the Tian Yuan Fund for Mathematics under Grand No 10426007, the Key Project of the Ministry of Education under Grant No. 106033, and National Science Foundation of China under.Grants Nos, 60372095 and 10272017. YTG would like to acknowledge the Cheung Kong Scholars Programme of the Ministry of Educ＇atlon of China and Li Ka Shing Foundation of Hong Kong
文摘A spherical Kadomtsev-Petviashvili （SKP） equation for dust acoustic or ion-acoustic waves is studied. Similarity reductions of the SKP equation are obtained with the one-parameter （ε） Lie group of infinitesimal transformations and Clarkson-Kruskal direct method, The SKP equation is also solved with a generalized tanh function method.
