On the solvability of a class of boundary value problems for systems of the integral equations with power nonlinearity on the whole axis

We investigate a class of boundary value problems for systems of convolution type integral equations on the whole axis with power nonlinearity. These problems have a direct application in the $p$-adic theory of open-closed strings. We prove the existence of odd rolling solutions to the problems. We also establish the integral asymptotic for the constructed solutions. The results are illustrated by examples of the equations under consideration.