<正> A spherical Kadomtsev-Petviashvili (SKP) equation for dust acoustic or ion-acoustic waves is studied.Sim-ilarity reductions of the SKP equation are obtained with the one-parameter (ε) Lie group of infinite...<正> A spherical Kadomtsev-Petviashvili (SKP) equation for dust acoustic or ion-acoustic waves is studied.Sim-ilarity reductions of the SKP equation are obtained with the one-parameter (ε) Lie group of infinitesimal transformationsand Clarkson-Kruskal direct method.The SKP equation is also solved with a generalized tanh function method.展开更多
<Abstract>In this paper,under the Painlevé-integrable condition,the auto-Bcklund transformations in different forms for a variable-coefficient Korteweg-de Vries model with physical interests are obtained ...<Abstract>In this paper,under the Painlevé-integrable condition,the auto-Bcklund transformations in different forms for a variable-coefficient Korteweg-de Vries model with physical interests are obtained through various methods including the Hirota method,truncated Painlevé expansion method,extended variable-coefficient balancing-act method,and Lax pair.Additionally,the compatibility for the truncated Painlevé expansion method and extended variable-coefficient balancing-act method is testified.展开更多
The Caudrey-Dodd-Gibbon-Kotera Sawada (CDGKS) equation has attracted many physicists and mathematicians. In this paper, based on the idea of variable-coefficient balancing-act method and the computerized .symbolic com...The Caudrey-Dodd-Gibbon-Kotera Sawada (CDGKS) equation has attracted many physicists and mathematicians. In this paper, based on the idea of variable-coefficient balancing-act method and the computerized .symbolic compu tation, some exact analytic solutions for the CDGKS equation have been obtained.展开更多
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<正> A spherical Kadomtsev-Petviashvili (SKP) equation for dust acoustic or ion-acoustic waves is studied.Sim-ilarity reductions of the SKP equation are obtained with the one-parameter (ε) Lie group of infinitesimal transformationsand Clarkson-Kruskal direct method.The SKP equation is also solved with a generalized tanh function method.
基金supported by the Key Project of the Ministry of Education under Grant No.106033Specialized Research Fund for the Doctoral Program of Higher Education under Grant No.20060006024+2 种基金Ministry of Education,National Natural Science Foundation of China under Grant Nos.60372095 and 60772023Open Fund of the State Key Laboratory of Software Development Environment under Grant No.SKLSDE-07-001Beijing University of Aeronautics and Astronautics,and National Basic Research Program of China (973 Program) under Grant No.2005CB321901
文摘<Abstract>In this paper,under the Painlevé-integrable condition,the auto-Bcklund transformations in different forms for a variable-coefficient Korteweg-de Vries model with physical interests are obtained through various methods including the Hirota method,truncated Painlevé expansion method,extended variable-coefficient balancing-act method,and Lax pair.Additionally,the compatibility for the truncated Painlevé expansion method and extended variable-coefficient balancing-act method is testified.
基金This workis supported by the National Natural Science Foundation of China under Grant (60372095)by the science and technology development pro-gramof Beijing Municipal Commission of Education (KM200410772002)by the Beijing Excellent Talent Fund.
文摘The Caudrey-Dodd-Gibbon-Kotera Sawada (CDGKS) equation has attracted many physicists and mathematicians. In this paper, based on the idea of variable-coefficient balancing-act method and the computerized .symbolic compu tation, some exact analytic solutions for the CDGKS equation have been obtained.
