EXACT SOLUTIONS OF THE TWO-DIMENSIONAL KONOPELCHENKO-DUBROVSKY EQUATION - Syzdykova, А.; Razina, О.; Burgumbayeva, С. (Bulletin of Abai KazNPU. Series of Physical and Mathematical sciences, 2023)
The study of exact solutions of the equations of mathematical physics occupies a very important place in the explanation of certain physical phenomena. The variety of solutions to the equations of mathematical physics associated with the use of various mathematical methods is very important for many sciences, such as chemistry, biology, fluid mechanics, optical fibers, space technology, control engineering, fluid dynamics, meteorology, plasma physics, applied mathematics and computer science. In recent years, most researchers have improved several methods for obtaining exact solutions to the equations of mathematical physics, such as the Darboux transformation method, the exponential function method, the hyperbolic tangent method, the Hirota method, the generalized Kudryashov method, and many others. In this paper, the two-dimensional Konopelchenko-Dubrovsky equation is studied. The study of this equation is relevant due to the fact that it has an application in physics, namely, it describes the evolution of dispersive waves of small amplitude arising in shallow water, and this equation can also be considered as a generalized form of the Kadomtsev-Petviashvili equation, the modified Kadomtsev-Petviashvili equation, the Gardner equation. To obtain exact solutions, the sine-cosine method was used. It is shown that the sine-cosine method is an effective mathematical tool for finding exact solutions to equations of mathematical physics. New solutions in the form of periodic waves are obtained. Graphs of the obtained solutions are presented in figures.