The matrix Lax representation of the generalized Riemann equations and its conservation Laws

Abstract

It is shown that the generalized Riemann equation is equivalent with the multicomponent generalization of the Hunter - Saxton equation. New matrix and scalar Lax representation is presented for this generalization. New class of the conserved densities, which depends explicitly on the time are obtained directly from the Lax operator. The algorithm, which allows us to generate a big class of the non-polynomial conservation laws of the generalized Riemann equation is presented. Due to this new series of conservation laws of the Hunter-Saxton equation is obtained.

The change the title, added references, corrected typos. To appear in Phys.Lett A

References in corpus (3)

• Differential-Algebraic Integrability Analysis of the Generalized Riemann Type and Korteweg-de Vries Hydrodynamical Equations
• The non-polynomial conservation laws and integrability analysis of generalized Riemann type hydrodynamical equations
• The Hunter-Saxton equation: remarkable structures of symmetries and conserved densities

Cited by in corpus (5)

• The differential-algebraic and bi-Hamiltonian integrability analysis of the Riemann type hierarchy revisited
• Conservation laws and symmetries of Hunter-Saxton equation: revisited
• Conservation laws of the generalized Riemann equations at $N=2,3,4$
• On the Complete Integrability of a One Generalized Riemann Type Hydrodynamic System
• On the Complete Integrability of Nonlinear Dynamical Systems on Discrete Manifolds within the Gradient-Holonomic Approach