Integrable Dispersive Chains and Energy Dependent Schrodinger Operator

Abstract

In this paper we consider integrable dispersive chains associated with the so called Energy Dependent Schrodinger operator. In a general case multi component reductions of these dispersive chains are new integrable systems, which are characterised by two arbitrary natural numbers. Also we show that integrable three dimensional linearly degenerate quasilinear equations of a second order possess infinitely many differential constraints. Corresponding dispersive reductions are integrable systems associated with the Energy Dependent Schrodinger operator.

References in corpus (11)

• Integrable hydrodynamic chains
• Hydrodynamic reductions and solutions of a universal hierarchy
• Energy-dependent potentials revisited: A universal hierarchy of hydrodynamic type
• Towards a theory of differential constraints of a hydrodynamic hierarchy
• Dispersive deformations of hydrodynamic reductions of 2D dispersionless integrable systems
• Algebro-geometric approach in the theory of integrable hydrodynamic type systems
• Classification of integrable hydrodynamic chains and generating functions of conservation laws
• The model equation of soliton theory
• The Hamiltonian approach in classification and integrability of hydrodynamic chains
• Integrable equations in 2+1-dimensions: deformations of dispersionless limits
• Classification of integrable Hamiltonian hydrodynamic chains associated with Kupershmidt's brackets

Cited by in corpus (2)

• The integrable heavenly type equations and their Lie-algebraic structure
• Integrable Dispersive Chains and Their Multi-Phase Solutions