Why do soliton equations come in hierarchies?

DOI10.1063/1.530024zbMath0780.35095OpenAlexW2040382467MaRDI QIDQ3141397

Russi G. Yordanov

Publication date: 6 December 1993

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/10919/47100

zbMATH Keywords

eigenfunctionsrecursion operatorcomplete integrabilityhierarchy of nonlinear evolution equationsLax pairslinear spectral problemoperator identity

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Soliton equations (35Q51)

Cites Work

• Nonlinear evolution equations associated with energy-dependent Schrödinger potentials
• Schrödinger spectral problems with energy–dependent potentials as sources of nonlinear Hamiltonian evolution equations
• Cauchy problem for the linearized version of the Generalized Polynomial KdV equation
• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems

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