On transforms reducing one-dimensional systems of shallow-water to the wave equation with sound speed c 2 = x
Tóm tắt
We obtain point transformations for three one-dimensional systems: shallow-water equations on a flat and a sloping bottom and the system of linear equations obtained by formal linearization of shallow-water equations on a sloping bottom. The passage of these systems to the Carrier-Greenspan parametrization is also obtained. For linear shallow-water equations on a sloping bottom, we obtain the solution in the form of a traveling wave with variable velocity. We establish the relationship between the resulting solution and the solution of the two-dimensional wave equation.
Tài liệu tham khảo
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