【摘要】 从具有较多参数的复杂非线性方程的解出发,取某些参数的极限,这些解就退化到具有较少参数的简单方程的解,本文以KdV方程的行波解为例说明对于某些特解,上述极限过程的逆过程,即将简单方程的解形变到复杂方程的解是可能的,但一般来说并不一定具有唯一性。更多还原

【Abstract】 By means of some limiting procedures, the solutions of a complex nonlinear equation with many parameters could degenerate into the solutions of a simple equation with less parameters. In this paper, taking KdV equation and high order KdV equations as example, we analyse the possibility of the inverse procedure of the limiting process mentioned above. The results show that deforming a solution of a simple equation into that of the. complex equations is possible. However, this inverse procedure is not unique in general.更多还原