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A novel symmetry constraint of the super cKdV system. (English) Zbl 1203.35253
Summary: A new $(1+1)$-dimensional integrable system, i.e. the super coupled Korteweg-de Vries (cKdV) system, has been constructed by a super extension of the well-known $(1+1)$-dimensional cKdV system. For this new system, a novel symmetry constraint between the potential and the eigenfunction can be obtained by means of the binary nonlinearization of its Lax pairs. The constraints for even variables are explicit and the constraints for odd variables are implicit. Under the symmetry constraint, the spacial part and the temporal parts of the equations associated with the Lax pairs for the super cKdV system can be decomposed into the super finite-dimensional integrable Hamiltonian systems on the supersymmetry manifold $R^{4N|2N + 2}$, whose integrals of motion are explicitly given.

MSC:
35Q53KdV-like (Korteweg-de Vries) equations
37K10Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies
35K40Systems of second-order parabolic equations, general
35C07Traveling wave solutions of PDE
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