The model equation of soliton theory

Abstract

We consider an hierarchy of integrable 1+2-dimensional equations related to Lie algebra of the vector fields on the line. The solutions in quadratures are constructed depending on $n$ arbitrary functions of one argument. The most interesting result is the simple equation for the generating function of the hierarchy which defines the dynamics for the negative times and also has applications to the second order spectral problems. A rather general theory of integrable 1+1-dimensional equations can be developed by study of polynomial solutions of this equation under condition of regularity of the corresponding potentials.

17 p

References in corpus (1)

• An integrable hierarchy with a perturbed Henon-Heiles system

Cited by in corpus (5)

• The four-dimensional Martinez Alonso--Shabat equation: reductions and nonlocal symmetries
• Symmetry reductions and exact solutions of Lax integrable $3$-dimensional systems
• Integrable Dispersive Chains and Energy Dependent Schrodinger Operator
• 3D-consistency of negative flows
• Integrable Dispersive Chains and Their Multi-Phase Solutions