Negative flows for several integrable models

Abstract

A construction of negative flows for integrable systems based on the Lax representation and squared eigenfunctions is proposed. Examples considered include the Boussinesq equation and its reduction to the Sawada-Kotera and Kaup-Kupershmidt equations; one of the Drinfeld-Sokolov systems and its reduction to the Krichever-Novikov equation.

arXiv comment15 pages

References in corpus (9)

• On Construction of Recursion Operators From Lax Representation
• The Camassa-Holm Equation: A Loop Group Approach
• On negative flows of the AKNS hierarchy and a class of deformations of bihamiltonian structure of hydrodynamic type
• Integrable KdV Systems: Recursion Operators of Degree Four
• On generating functions in the AKNS hierarchy
• Towards the theory of integrable hyperbolic equations of third order
• Nonautonomous symmetries of the KdV equation and step-like solutions
• Non-autonomous reductions of the KdV equation and multi-component analogs of the Painlevé equations P${}_{34}$ and P${}_3$
• Negative flows and non-autonomous reductions of the Volterra lattice

Cited by in corpus (3)

• 3D-consistency of negative flows
• Generalized Riemann-Hilbert-Birkhoff Decomposition and a New Class of Higher Grading Integrable Hierarchies
• New soliton solutions for Chen-Lee-Liu and Burgers hierarchies and its Bäcklund transformations