A new functional iterative algorithm for the regularized long-wave equation using an integral equation formalism
The author investigates the third-order nonlinear partial differential equation \( \eta_{t} + c_{0}\eta_{x} + \frac{3c_{0}}{2h_{0}}\eta\eta_{x} - \frac{h_{0}^{2}}{6}\eta_{xxt} = 0 \), describing some class of waves in shallow water. Here, \(\eta\) denotes the wave elevation and the other values describe physical characteristics of the process. It is proved that the solution of this equation (together with some initial conditions) satisfies a system of nonlinear integral equations. If the corresponding integral operator acting in some Banach space is contractive, then the classical iterative process permits to obtain solutions of the differential equation under consideration. The paper contains results of numerous computational experiments.
nonlinear integral equations of second kind
scientific article; zbMATH DE number 6859533
scientific article