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A family of nonlinear conservative finite difference schemes for the multidimensional Boussinesq Paradigm Equation is considered. A second order of convergence and a preservation of the discrete energy for this approach are proved. Existence and boundedness of the discrete solution on an appropriate time interval are established. The schemes have been numerically tested on the models of the propagation of a soliton and the interaction of two solitons. The numerical experiments demonstrate that the...
A three-parameter family of Boussinesq type systems in two space
dimensions is considered. These systems approximate the
three-dimensional Euler equations, and consist of three nonlinear
dispersive wave equations that describe two-way propagation of
long surface waves of small amplitude in ideal fluids over a
horizontal bottom. For a subset of these systems it is proved that
their Cauchy problem is locally well-posed in suitable Sobolev
classes. Further, a class of these systems is discretized...
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