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Point symmetries of conditionally integrable nonlinear evolution equations. (English) Zbl 0722.58026

Summary: The Lie point symmetries of the first two equations in the Kadomtsev- Petviashvili (KP) hierarchy, introduced by M. Jimbo and T. Miwa [Publ. Res. Inst. Math. Sci. 19, 943-1001 (1983; Zbl 0557.35091)] are investigated. The first is the potential KP equation, the second involves four independent variables and is called the Jimbo-Miwa (JM) equation. The joint symmetry algebra for the two equations is shown to have a Kac-Moody-Virasoro structure, whereas the symmetry algebra of the JM equation alone does not. Subgroups of the joint symmetry group are used to perform symmetry reduction and to obtain invariant solutions.

MSC:

37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
35Q58 Other completely integrable PDE (MSC2000)
17B67 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras

Citations:

Zbl 0557.35091
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References:

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