Discrete Boussinesq equations
Seminar Room 1, Newton Institute
AbstractWe discuss lattice versions of the Boussinesq equation. Since the continuous form is not evolutionary (i.e., first order in time derivatives) but second order in time, the Boussinesq equation cannot be discretized as a one-component equation on an elementary quadrilateral of the Cartesian lattice. Instead there are one-component discretizations on a 3 x 3 stencil and three-component versions on the quadrilateral. Furthermore, discrete bilinear versions are also known. We compare these different approaches and the related soliton solutions.
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