| Summary: | 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 2×2 matrices.
Results. A new integrable system of wave interaction is obtained. For dimension
2×2, 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.
|
|---|
