Integration of a mixed problem on the half-axis for the system of Kaup equations

Abstract A system of nonlinear Kaup equations on the half-axis is considered in the class of functions rapidly decreasing with respect to the spatial variable. An equation is derived for describing the evolution of the Weyl function of a quadratic pencil of Sturm–Liouville equations on the half-axis, whose coefficients are the solution of a mixed problem posed for the system of nonlinear Kaup equations. The obtained results allow the integration of the system of nonlinear Kaup equations on the half-axis using the inverse scattering method. An algorithm for solving the mixed problem for the nonlinear Kaup system in the class of functions rapidly decreasing with respect to the spatial variable is obtained.

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