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
The homogeneous balance method is a method for solving genera/partial differential equations (PDEs). In this paper we solve a kind of initial problems of the PDEs by using the special Baecklund transformations of the ...The homogeneous balance method is a method for solving genera/partial differential equations (PDEs). In this paper we solve a kind of initial problems of the PDEs by using the special Baecklund transformations of the initial problem. The basic Fourier transformation method and some variable-separation skill are used as auxiliaries. Two initial problems of Nizlmich and the Nizlanich-Novikov-Veselov equations are solved by using this approach.展开更多
A modified homogeneous balance method is proposed by improving some key steps in the homogeneousbalance method.Bilinear equations of some nonlinear evolution equations are derived by using the modified homogeneousbala...A modified homogeneous balance method is proposed by improving some key steps in the homogeneousbalance method.Bilinear equations of some nonlinear evolution equations are derived by using the modified homogeneousbalance method.Generalized Boussinesq equation,KP equation,and mKdV equation are chosen as examples to illustrateour method.This approach is also applicable to a large variety of nonlinear evolution equations.展开更多
A nonlinear transformation and some multi-solition solutions for the (2+1 )-dimensional generalized Broer-Kaup (GBK) system is first given by using the homogeneous balance method. Then starting from the nonlinear tran...A nonlinear transformation and some multi-solition solutions for the (2+1 )-dimensional generalized Broer-Kaup (GBK) system is first given by using the homogeneous balance method. Then starting from the nonlinear transformation, we reduce the (2+ 1)-dimensional GBK system to a simple linear evolution equation. Solving this equation,we can obtain some new explicit exact solutions of the original equations by means of the extended hyperbola function method.展开更多
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.
文摘The homogeneous balance method is a method for solving genera/partial differential equations (PDEs). In this paper we solve a kind of initial problems of the PDEs by using the special Baecklund transformations of the initial problem. The basic Fourier transformation method and some variable-separation skill are used as auxiliaries. Two initial problems of Nizlmich and the Nizlanich-Novikov-Veselov equations are solved by using this approach.
基金Supported by the National Natural Science Foundation of China under Grant No. 11071209the Natural Science Foundation of the Higher Education Institutions of Jiangsu Province under Grant No. 10KJBll0011
文摘A modified homogeneous balance method is proposed by improving some key steps in the homogeneousbalance method.Bilinear equations of some nonlinear evolution equations are derived by using the modified homogeneousbalance method.Generalized Boussinesq equation,KP equation,and mKdV equation are chosen as examples to illustrateour method.This approach is also applicable to a large variety of nonlinear evolution equations.
文摘A nonlinear transformation and some multi-solition solutions for the (2+1 )-dimensional generalized Broer-Kaup (GBK) system is first given by using the homogeneous balance method. Then starting from the nonlinear transformation, we reduce the (2+ 1)-dimensional GBK system to a simple linear evolution equation. Solving this equation,we can obtain some new explicit exact solutions of the original equations by means of the extended hyperbola function method.
