Integrable Theory of the Perturbation Equations

Abstract

An integrable theory is developed for the perturbation equations engendered from small disturbances of solutions. It includes various integrable properties of the perturbation equations: hereditary recursion operators, master symmetries, linear representations (Lax and zero curvature representations) and Hamiltonian structures etc. and provides us a method to generate hereditary operators, Hamiltonian operators and symplectic operators starting from the known ones. The resulting perturbation equations give rise to a sort of integrable coupling of soliton equations. Two examples (MKdV hierarchy and KP equation) are carefully carried out.

27 pages, latex, to appear in Chaos, Soliton & Fractals

References in corpus (1)

• The Bi-Hamiltonian Structure of the Perturbation Equations of KdV Hierarchy

Cited by in corpus (14)

• Semi-direct sums of Lie algebras and discrete integrable couplings
• A discrete variational identity on semi-direct sums of Lie algebras
• Trigonal curves and algebro-geometric solutions to soliton hierarchies
• A Bi-Hamiltonian Formulation for Triangular Systems by Perturbations
• Extending Hamiltonian Operators to Get Bi-Hamiltonian Coupled KdV Systems
• Graded Symmetry Algebras of Time-Dependent Evolution Equations and Application to the Modified KP equations
• A Class of Coupled KdV systems and Their Bi-Hamiltonian Formulations
• Integrable systems with BMS${}_3$ Poisson structure and the dynamics of locally flat spacetimes
• Completion of the Ablowitz-Kaup-Newell-Segur integrable coupling
• A perturbative approach to a class of Fokker-Planck equations
• Extension of Hereditary Symmetry Operators
• Non-autonomous Svinolupov Jordan KdV Systems
• Construction and separability of nonlinear soliton integrable couplings
• The Method of ${\mathcal{M}}_n$-Extension: The KdV Equation