On one nonlinear integrable model of wave interaction

Background. In this work, the functional method is applied to a first-order matrix system and the corresponding equations of wave dynamics are derived. The aim of the work is the conclusion and analysis of a new integrable Burgers-type wave interaction system.
Materials and methods. The main method used in this work is the method of functional permutations in matrix form. The general form of matrix equations is presented for an arbitrary finite matrix dimension. A detailed analysis of the equations in an exploded form is presented for the dimension of $2\times2$ matrices.
Results. A new integrable system of wave interaction is obtained. For dimension $2\times2$, the equations are written in component form. A reduced system is constructed, like a three-wave interaction system. The general form of exact solutions for the reduced system is found. Concrete examples of real non-singular solutions are given.
Conclusions. Using the method of functional substitutions, a new integrable system of wave interaction was found, which is useful for practical use in applied problems.