An Integral Equation Formalism for Integrating a Nonlinear Initial-Boundary Value Problem for a Boussinesq Equation

Abstract EN

In this paper, a new nonlinear initial-boundary value problem for a Boussinesq equation is formulated.

And a coupled system of nonlinear integral equations, equivalent to the new initial-boundary value problem, is constructed for integrating the initial-boundary value problem, but which is inherently different from other conventional formulations for integral equations.

For the numerical solutions, successive approximations are applied, which leads to a functional iterative formula.

A propagating solitary wave is simulated via iterating the formula, which is in good agreement with the known exact solution.