We propose a new method for solving the Gelfand-Levitan-Marchenko equation (GLME) based on the block version of the Toeplitz Inner-Bordering (TIB) with an arbitrary point to start the calculation. This makes it possible to find solutions of the GLME at an arbitrary point with a cutoff of the matrix coefficient, which allows to avoid the occurrence of numerical instability and to perform calculations for soliton solutions spaced apart in the time domain. Using an example of two solitons, we demonstrate our method and its range of applicability. An example of eight solitons shows how the method can be applied to a more complex signal configuration.
翻译:我们根据Teeplitz In-Neconfronting(TIB)的区块版提出一种新的方法来解决Gelfand-Levitan-Marchenko等式(GLME),该方程式有一个任意的起始点,可以任意找到GLME的解决方案,并切断基数系数,从而避免数字不稳定的发生,并对在时间域间间间隔的索利顿解决办法进行计算。我们以两个索利顿为例,展示了我们的方法及其适用范围。八个索利顿的例子显示了该方法如何适用于更为复杂的信号配置。