Solitons and Bound States of the Time-Independent Schrödinger Equation

Abstract

A numerical calculation validates the correspondence between the soliton nonlinear asymptotic solutions of the time-dependent Korteweg-deVries equation and the bound states of the one-dimensional time-independent Schr\"odinger equation. Here the attractive potential of the Schr\"odinger equation is equal to the initial condition of the Korteweg-deVries equation. A situation is examined where an oscillatory state remains after solitons have emerged.