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Mathematical Formulation of Inverse Scattering and Korteweg-De Vries Equation

机译：逆散射和Korteweg-De Vries方程的数学公式

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Inverse scattering refers to the determination of the solutions of a set of differential equations based on known asymptotic solutions, that is, the solution of Marchenko equation. Marchenko equation was derived using integral equation. The potential function derived from eigenvalues and scattering data seems to be the inverse method of scattering problem. The reflection coefficient with one pole and zero reflection coefficients has been chosen to solve inverse scattering problem. Again this paper deals with the connection between inverse scattering and the Korteweg-de Vries equation and describes variety of examples with Korteweg-de Vries equation: the single-soliton solution, the two-soliton solution and finally the N-soliton solution. Throughout the work, the primary objective is to study some mathematical techniques applied in analyzing the behavior of soliton in the KdV equations. Keywords: Marchenko equation, KdV equation, Solitons, Scattering, Inverse Scattering, Canal.
机译：逆散射是指根据已知的渐近解（即Marchenko方程的解）确定一组微分方程的解。 Marchenko方程是使用积分方程推导的。从特征值和散射数据得出的势函数似乎是散射问题的逆方法。选择具有一极和零反射系数的反射系数来解决反散射问题。本文再次讨论了反向散射与Korteweg-de Vries方程之间的联系，并描述了Korteweg-de Vries方程的各种例子：单孤子解，双孤子解，最后是N孤子解。在整个工作中，主要目标是研究一些用于分析KdV方程中孤子行为的数学技术。关键字：Marchenko方程，KdV方程，孤子，散射，逆散射，运河。

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