Asymptotic Behavior of Solutions of a System of KdV Type Associated with the Schrödinger Operator with an Energy-Dependent Potential

In this paper, we study the asymptotic behavior of the solutions of the Cauchy problem for a nonlinear KdV type system associated with the Schrödinger spectral operator with an energy-dependent potential. Using the set of motion integrals for this system, we determine the amplitude of the asymptotic solution in terms of spectral data for the initial condition of the Cauchy problem.