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### An Integral Equation Approach to the Fully Nonlinear Fluid Flow Problem in an Infinite Channel Over Arbitrary Bottom Topography

#### Abstract

The fully nonlinear two-dimensional fluid flow problem involving an infinite channel with arbitrary bottom topography is handled for its complete solution. The nonlinear boundary value problem under consideration involves an unknown boundary comprising the top surface of the fluid and its solution is determined by utilizing a formulation in the form of a Dirichlet's problem for the two-dimensional Laplace's equation to be satisfied by the velocity potential of the irrotational flow in question in which the complete boundary is not known beforehand. The whole mathematical problem is cast into a coupled system of singular integral equations of the Cauchy type involving unknown curves of integration and finally the numerical solutions of these integral equations are determined along with the parametric representations of the unknown curve, representing the upper surface of the fluid.