Korteweg-de Vries Equation; Asymptotic Behavior of Solutions

  title={Korteweg-de Vries Equation; Asymptotic Behavior of Solutions},
  author={Shunichi Tanaka},
In [9] and [10], we have studied the initial value problem for the Korteweg-de Vries (KdV) equation (1.1) ut—6uu x +u xxx =0 by the inverse scattering method. In this paper we study the asymptotic behavior of the solutions as t— >zh°°-Consider the Schrodinger equation (1.2) over (— oo } oo) with the potential u(x) satisfying (1.3) (throughout the paper integration is taken over (— oo, oo) unless otherwise indicated). If Im £2^0, there exist unique solution f±(x t £), of (1.2), called the Jost… CONTINUE READING