A method for practical realization of the inverse scattering transform method for the Korteweg-de Vries equation is proposed. It is based on analytical representations for Jost solutions and for integral kernels of transformation operators obtained recently by the authors. The representations have the form of functional series in which the first coefficient plays a crucial role both in solving the direct scattering and the inverse scattering problems. The direct scattering problem reduces to computation of a number of the coefficients following a simple recurrent integration procedure with a posterior calculation of scattering data by well known formulas. The inverse scattering problem reduces to a system of linear algebraic equations from which the first component of the solution vector leads to the recovery of the potential. We prove the applicability of the finite section method to the system of linear algebraic equations and discuss numerical aspects of the proposed method. Numerical examples are given, which reveal the accuracy and speed of the method.

翻译：为Korteweg-de Vries等式提出了一种实际实现反散射变异法的方法,它基于对Jost溶液和变异操作器整体内核的分析表述,是作者最近获得的。这些表述的形式是功能系列,第一个系数在解决直接散射和反散射问题方面发挥着关键作用。直接散射问题减少为在采用众所周知的公式对散射数据进行后方计算,经过简单的重复整合程序计算若干系数。反散射问题减少为线形代数方程式系统,而解决办法矢量器的第一个组成部分从该系统中恢复潜力。我们证明有限区法对线形变异方程式系统的适用性,并讨论拟议方法的数值方面。提供了数字实例,表明该方法的准确性和速度。