Collapse in the asymptotics of the solution to the complex Korteweg-de Vries equation

The work is devoted to the study of the asymptotic behavior of solutions to the Cauchy problem for the Korteweg-de Vries equation $u_t=u_{xxx}+6uu_x$ with complex initial data. It was found that, in contrast to the real solution, the asymptotic behavior of the complex solution in the dispersion region has collapses. The paper analyzes the asymptotic solution in the vicinity of such a point.