Numerical study of the supercritical solution of the stationary forced Korteweg-de Vries (sfKdV) equation
The time independent surface waves on a two dimensional incompressible and inviscid fluid flow passing over a bump on a flat bottom are considered. The stationary forced Korteweg-de Vries (fKdV) equation is defined in an unbounded interval. In this project, this unbounded interval is considered as three parts - on the bump, left hand side of the bump and right hand side of the bump. Exact boundary conditions are applied to the end points of the bump. All the possible combination of boundary conditions are used. A numerical approach is proposed to find the solitary wave solutions of fKdV equation by solving the boundary value problem on the bump. Then the solitary wave solutions are found in an extended interval. Using this new method, some new and exciting results are found.
Dey, Sumi, "Numerical study of the supercritical solution of the stationary forced Korteweg-de Vries (sfKdV) equation" (2015). ETD Collection for University of Texas, El Paso. AAI10010973.