Zakharov-Shabat反散射方程的不可约形式

An Irreducible Form of the Zakharov-Shabat Equations of Inverse Scattering Problem

对求孤子解的Z-S反散射方程组,给出了它的等价的不可约形式。在求N-孤子解时,Z-S方程组由2N个线性代数方程组成,求解手续就是计算一个2N×2N矩阵之逆。而本文所得的它的不可约形式,是由N个线性代数方程组成的,求解只需计算一个N×N矩阵之逆,从而使计算量大大缩小。文未给出求两孤子解和呼吸子解的实际的简单计算和结果。

An irreducible form of the Zakharov-Shabat equations of the inverse scattering problem for finding soliton solutions is given. In the case of N-soliton, the Zakharov-Shabat equations consist of 2N linear algebraic equations and one needs to find the inverse of a 2N×2N matrix. However, the irreducible form of them given in the present paper only consists of N linear algebraic equations and one thus needs to find the inverse of a N×N matrix. This will considerably reduces the amount of calculation The simple processes of finding one-, two-soliton solutions and breather solutions are shown by using the irreducible form.