Initial-boundary value problems for one-dimensional Nonlinearly dispersive shallow water equations in the Aleshkov model

Source abstract

The work considers a layer of liquid bounded by a free surface and a horizontal impermeable bottom. As a mathematical model, one-dimensional nonlinearly dispersive shallow water equations are used. For the system, a Cauchy problem with additional boundary conditions is formulated. A theorem on the existence and uniqueness of the solution to the initial-boundary value problem is proved. Then, the solution to this problem is constructed as a power series. The coefficients of the series are found by integrating ordinary differential equations. Particular solutions of initial-boundary value problems with various initial and boundary conditions are also obtained in the form of power series.