Asymptotic behavior of solutions of a system of the KdV type associated with the Schrödinger operator with an energy-dependent potential

In this paper, we continue to study the asymptotic behavior of solutions to the Cauchy problem for a nonlinear KdV-type system
$$ -v_t=-\frac{1}{4}u_{xxx}+vu_x+\frac{1}{2}uv_x, \ \ -u_t=\frac{3}{2}uu_x+v_x, $$
associated with the spectral Schrodinger operator with an energy-dependent potential. In the previous paper (see [10]), using a set of integrals of motion for this system, we found the amplitude of the asymptotic solution through the spectral data for the initial condition of the Cauchy problem. In the present paper, using another method (Zakharov and Manakov), we obtain an expression not only for the amplitude, but also for the phase of the solution of the KdV-type system.