Binary Symmetry Constraints of N-wave Interaction Equations in 1+1 and 2+1 Dimensions

Abstract

Binary symmetry constraints of the N-wave interaction equations in 1+1 and 2+1 dimensions are proposed to reduce the N-wave interaction equations into finite-dimensional Liouville integrable systems. A new involutive and functionally independent system of polynomial functions is generated from an arbitrary order square matrix Lax operator and used to show the Liouville integrability of the constrained flows of the N-wave interaction equations. The constraints on the potentials resulting from the symmetry constraints give rise to involutive solutions to the N-wave interaction equations, and thus the integrability by quadratures are shown for the N-wave interaction equations by the constrained flows.

41 pages, Latex

References in corpus (1)

• Separation of variables for soliton equations via their binary constrained flows

Cited by in corpus (4)

• Binary Nonlinearization of the Super Akns System Under an Implicit Symmetry Constraint
• Liouville integrability of the finite dimensional Hamiltonian systems derived from principal chiral field
• The Lax Integrable Differential-Difference Dynamical Systems on Extended Phase Spaces
• Finite dimensional Hamiltonian system related to Lax pair with symplectic and cyclic symmetries