A Novel Symmetry Constraint Of The Super cKdV System

TL;DR

This paper introduces a new super cKdV system by extending the classical cKdV system with supersymmetry, deriving a symmetry constraint via binary nonlinearization, and decomposing the system into finite-dimensional integrable Hamiltonian systems.

Contribution

It constructs a novel super cKdV system, establishes a unique symmetry constraint, and decomposes it into finite-dimensional integrable Hamiltonian systems on a supersymmetry manifold.

Findings

Explicit constraints for even variables derived.

Implicit constraints for odd variables established.

Decomposition into finite-dimensional integrable Hamiltonian systems achieved.

Abstract

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 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.