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The integrable system related to a third-order eigenvalue problem and involutive solution

Lanxin Chen

Abstract

A new type finite-dimensional system associated with a third-order eigenvalue problem is presented by means of the nonlinearized Lax pairs.Based on the generating function of integrals of motion,the resulting system is further improved to be completely integrable in the Liouville sense.Moreover,the involutive solutions of the evolution equations are given.

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Available abstract

Key concepts: Integrable system, Eigenvalues and eigenvectors, Order (exchange), Mathematics, Third order, Type (biology), Function (biology), Applied mathematics