Recently, a new decomposition of the -dimensional Kadomtsev?Petviashvili (KP) equation to a -dimensional Broer?Kaup (BK) equation and a -dimensional high-order BK equation was presented by Lou and Hu. In our paper, a ...Recently, a new decomposition of the -dimensional Kadomtsev?Petviashvili (KP) equation to a -dimensional Broer?Kaup (BK) equation and a -dimensional high-order BK equation was presented by Lou and Hu. In our paper, a unified Darboux transformation for both the BK equation and high-order BK equation is derived with the help of a gauge transformation of their spectral problems. As application, new explicit soliton-like solutions with five arbitrary parameters for the BK equation, high-order BK equation and KP equation are obtained.展开更多
An explicit N-fold Darboux transformation for a coupled of derivative nonlinear Schrodinger equations is constructed with the help of a gauge transformation of spectral problems. As a reduction, the Darboux transforma...An explicit N-fold Darboux transformation for a coupled of derivative nonlinear Schrodinger equations is constructed with the help of a gauge transformation of spectral problems. As a reduction, the Darboux transformation for well-known Gerdjikov-Ivanov equation is further obtained, from which a general form of N-soliton solutions for Gerdjikov-Ivanov equation is given.展开更多
Two new applications of homogeneous balance(HB) method are presented.It is shown that HB method can be extended to search for the Baecklund transformations and similarity reductions of nonlinear partial differential e...Two new applications of homogeneous balance(HB) method are presented.It is shown that HB method can be extended to search for the Baecklund transformations and similarity reductions of nonlinear partial differential equations.The close relations among the HB method,Weiss-Tabor-Carnevale method and Clarkson-Kruskal direct reduction method are also found.KdV-MKdV equation is considered as an illustrative example,and its on kind of Backlund transformation,three kinds of similarity reductions and several kinds of travelling wave solutions are obtained by using extended HB method.展开更多
基金Chinese Key Research Plan 'Mathematical Mechanization and a Platform for Automated Reasoning'，上海市科委资助项目，中国博士后科学基金
文摘Recently, a new decomposition of the -dimensional Kadomtsev?Petviashvili (KP) equation to a -dimensional Broer?Kaup (BK) equation and a -dimensional high-order BK equation was presented by Lou and Hu. In our paper, a unified Darboux transformation for both the BK equation and high-order BK equation is derived with the help of a gauge transformation of their spectral problems. As application, new explicit soliton-like solutions with five arbitrary parameters for the BK equation, high-order BK equation and KP equation are obtained.
文摘An explicit N-fold Darboux transformation for a coupled of derivative nonlinear Schrodinger equations is constructed with the help of a gauge transformation of spectral problems. As a reduction, the Darboux transformation for well-known Gerdjikov-Ivanov equation is further obtained, from which a general form of N-soliton solutions for Gerdjikov-Ivanov equation is given.
文摘Two new applications of homogeneous balance(HB) method are presented.It is shown that HB method can be extended to search for the Baecklund transformations and similarity reductions of nonlinear partial differential equations.The close relations among the HB method,Weiss-Tabor-Carnevale method and Clarkson-Kruskal direct reduction method are also found.KdV-MKdV equation is considered as an illustrative example,and its on kind of Backlund transformation,three kinds of similarity reductions and several kinds of travelling wave solutions are obtained by using extended HB method.
