摘要
In this paper, based on Lax pair of Riccati form of the generalized KdV(GKdV) equation with external force term, a new auto-Darboux transformation (ADT) is derived. As the application of the ADT, only if integration is needed, a series of explicit analytic solutions can be obtained, which contain solitary-like wave solutions. This method may be important for seeking more new and physical signficant analytic solutions of nonlinear evolution equations.
基于 Ｒｉｃｃａｔｉ形式的 Ｌａｘ对，本文推得了含外力项的广义 ＫｄＶ方程的新自Ｄａｒｂｏｕｘ变换．当应用这个变换时，仅需要做积分，就能获得一系列显示解析解，其中包含类孤波解．这种途径对于寻找非线性发展方程新的具有物理意义的解或许是有用的．
基金
Supported by the National Natural Science Foundation of China under the Grant(19572022)
Doctoral Foundation of Education Mini
