KdV方程有反射初值问题非孤子尾部渐近式的一种解法

将KdV方程有反射初值问题之解表示为孤子部分与非孤子部分之和.相对孤子假定非孤子部分为小量,使其满足的方程线性化,用富氏变换直接求得依赖于初值的非孤子渐近式.用适当的近似方法求得初值所对应的Schrödinger方程的分立谱后,由IST的结论得孤子表达式,从而构成KdV方程有反射势初值问题的解.并以某些初值实例计算得到了与文献一致的结果.

AN APPROACH TO THE ASYMPTOTIC SOLUTION OF OSCILLATORY TAIL OF REFLECTIVE INITIAL VALUE PROBLEM OF KdV EQUATION

Assume that the solution of KdV reflective initial value problem equals the sum of the pure-soliton part and the non-soliton part, and the latter is comparatively small. Then the equation satisfied by the non-soliton part is linearized and the solution of asymptotic oscillation form is obtained directly by means of Fourier Transformation. After solving the discrete spectrum of the time-independent Schodinger equation associated with the initial value by some proper method, the pure-soliton expression is available according to 1ST. Through the calculation of specific initial value examples, the results obtained in this paper are found to be consistent with those of the references.