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Derivation of conservation laws for a nonlinear wave equation modelling melt migration using Lie point symmetry generators. (English) Zbl 1110.35076
Summary: The derivation of conservation laws for a nonlinear wave equation modelling the migration of melt through the Earth’s mantle is considered. New conserved vectors which depend explicitly on the spatial coordinate are generated using the Lie point symmetry generators of the equation and known conserved vectors. It is demonstrated how conserved vectors that are conformally associated with a Lie point symmetry generator can be derived more simply than by the direct method by imposing the symmetry condition on the conservation law equation.

MSC:
35Q53 KdV equations (Korteweg-de Vries equations)
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
86A17 Global dynamics, earthquake problems (MSC2010)
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