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On the conservation laws and invariant solutions of the mKdV equation. (English) Zbl 1180.35471

Summary: We consider modified Korteweg-de Vries (mKdV) equation. By using the nonlocal conservation theorem method and the partial Lagrangian approach, conservation laws for the mKdV equation are presented. It is observed that only nonlocal conservation theorem method lead to the nontrivial and infinite conservation laws. In addition, invariant solution is obtained by utilizing the relationship between conservation laws and Lie-point symmetries of the equation.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
37K05 Hamiltonian structures, symmetries, variational principles, conservation laws (MSC2010)
35B06 Symmetries, invariants, etc. in context of PDEs
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