A modified version of the bilinear Bcklund transformation for the MKdV equation was given, with which some new solutions of the MKdV equation are obtained. The approach used here is general and can be applied to other...A modified version of the bilinear Bcklund transformation for the MKdV equation was given, with which some new solutions of the MKdV equation are obtained. The approach used here is general and can be applied to other soliton equations.展开更多
This paper is concerned with the (2+1)-dimensional Burgers' and heat types of equations.All of the geometic vector fields of the equations are obtained,an optimal system of the equation is presented.Especially,the...This paper is concerned with the (2+1)-dimensional Burgers' and heat types of equations.All of the geometic vector fields of the equations are obtained,an optimal system of the equation is presented.Especially,the Bcklund transformations (BTs) for the Burgers' equations are constructed based on the symmetry.Then,all of the symmetry reductions are provided in terms of the optimal system method,and the exact explicit solutions are investigated by the symmetry reductions and Bcklund transformations.展开更多
In this paper, the Hirota bilinear method is applied to a nonlinear equation which is a deformation to a KdV equation with a source. Using the Hirota’s bilinear operator, we obtain its bilinear form and construct its...In this paper, the Hirota bilinear method is applied to a nonlinear equation which is a deformation to a KdV equation with a source. Using the Hirota’s bilinear operator, we obtain its bilinear form and construct its bilinear Bcklund transformation. And then we obtain the Lax representation for the equation from the bilinear Bcklund transformation and testify the Lax representation by the compatibility condition.展开更多
The bilinear Bcklund transformation (BT) provides a means of finding multisoliton solutions of some non-linear evolution equations, where Hirota's technique is used. In this paper, the bilinear BT for Toda lattic...The bilinear Bcklund transformation (BT) provides a means of finding multisoliton solutions of some non-linear evolution equations, where Hirota's technique is used. In this paper, the bilinear BT for Toda lattice was modified and then some novel solutions of the Toda lattice was constructed through the modified BT.展开更多
Whitham–Broer–Kaup(WBK) equations in the shallow water small-amplitude regime is hereby under investigation. Nonlocal symmetry and Bcklund transformation are presented via the truncated Painlevé expansion.This ...Whitham–Broer–Kaup(WBK) equations in the shallow water small-amplitude regime is hereby under investigation. Nonlocal symmetry and Bcklund transformation are presented via the truncated Painlevé expansion.This residual symmetry is localised to Lie point symmetry by the properly enlarged system. The finite symmetry transformation of the prolonged system is computed. Based on the CTE method, WBK equations are linearized and new analytic interaction solutions between solitary waves and cnoidal waves are given with the aid of solutions for the linear equation.展开更多
文摘A modified version of the bilinear Bcklund transformation for the MKdV equation was given, with which some new solutions of the MKdV equation are obtained. The approach used here is general and can be applied to other soliton equations.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11171041 and 10971018the Natural Science Foundation of Shandong Province under Grant No.ZR2010AM029+1 种基金the Promotive Research Fund for Young and Middle-Aged Scientists of Shandong Province under Grant No.BS2010SF001the Doctoral Foundation of Binzhou University under Grant No.2009Y01
文摘This paper is concerned with the (2+1)-dimensional Burgers' and heat types of equations.All of the geometic vector fields of the equations are obtained,an optimal system of the equation is presented.Especially,the Bcklund transformations (BTs) for the Burgers' equations are constructed based on the symmetry.Then,all of the symmetry reductions are provided in terms of the optimal system method,and the exact explicit solutions are investigated by the symmetry reductions and Bcklund transformations.
文摘In this paper, the Hirota bilinear method is applied to a nonlinear equation which is a deformation to a KdV equation with a source. Using the Hirota’s bilinear operator, we obtain its bilinear form and construct its bilinear Bcklund transformation. And then we obtain the Lax representation for the equation from the bilinear Bcklund transformation and testify the Lax representation by the compatibility condition.
文摘The bilinear Bcklund transformation (BT) provides a means of finding multisoliton solutions of some non-linear evolution equations, where Hirota's technique is used. In this paper, the bilinear BT for Toda lattice was modified and then some novel solutions of the Toda lattice was constructed through the modified BT.
基金Supported by the Key Foundation of Anhui Education Bureau under Grant No.KJ2013A028the 211 Project of Anhhui University under Grant No.J18520104+2 种基金Scientific Training Project for University StudentsNational Natural Science Foundation of China under Grant Nos.11471015,11571016Natural Science Foundation of Anhui Province under Grant No.1408085MA02
文摘Whitham–Broer–Kaup(WBK) equations in the shallow water small-amplitude regime is hereby under investigation. Nonlocal symmetry and Bcklund transformation are presented via the truncated Painlevé expansion.This residual symmetry is localised to Lie point symmetry by the properly enlarged system. The finite symmetry transformation of the prolonged system is computed. Based on the CTE method, WBK equations are linearized and new analytic interaction solutions between solitary waves and cnoidal waves are given with the aid of solutions for the linear equation.
