Negative powers of Olver recursion operators

DOI10.1063/1.529234zbMath0734.35117OpenAlexW2017358916MaRDI QIDQ3361296

Publication date: 1991

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

Full work available at URL: https://doi.org/10.1063/1.529234

zbMATH Keywords

symmetries sinh-Gordon equation Miura transform inverse scattering solution negative order KdV equations

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Correspondences and other transformation methods (e.g., Lie-Bäcklund) for PDEs on manifolds (58J72)

Related Items (48)

Negative-order KdV equations in (3+1) dimensions by using the KdV recursion operator ⋮ Breather solutions of a negative order modified Korteweg-de Vries equation and its nonlinear stability ⋮ Novel variable separation solutions and exotic localized excitations via the ETM in nonlinear soliton systems ⋮ Integration of the negative order Korteweg–de Vries equation with a self-consistent source in the class of periodic functions ⋮ A formula for obtaining new hereditary symmetries and new integrable equations ⋮ Soliton scattering with amplitude changes of a negative order AKNS equation ⋮ Discrete Analogues of a Negative Order AKNS Equation ⋮ Painlevé analysis for a new integrable equation combining the modified Calogero-Bogoyavlenskii-Schiff (MCBS) equation with its negative-order form ⋮ On the nonlocal equations and nonlocal charges associated with the Harry Dym hierarchy ⋮ Residual symmetries and soliton-cnoidal wave interaction solutions for the negative-order Korteweg-de Vries equation ⋮ Abundant symmetries for the 1+1 dimensional classical Liouville field theory ⋮ Symmetries of the KdV equation and four hierarchies of the integrodifferential KdV equations ⋮ On a Riemann-Hilbert problem for the negative-order KdV equation ⋮ Variational bihamiltonian cohomologies and integrable hierarchies. III: Linear reciprocal transformations ⋮ Negative order mKdV equation and \(N\)-solitons ⋮ A new integrable equation combining the modified KdV equation with the negative-order modified KdV equation: multiple soliton solutions and a variety of solitonic solutions ⋮ Negative flows of generalized KdV and mKdV hierarchies and their gauge-Miura transformations ⋮ A variety of negative-order integrable KdV equations of higher orders ⋮ Explicit soliton–cnoidal wave interaction solutions for the (2+1)-dimensional negative-order breaking soliton equation ⋮ Repeated application of the recursion operator for a new hierarchy of negative-order integrable KdV equations ⋮ Wave solutions to an integrable negative order KdV equation ⋮ Integration of the negative order Korteweg-de Vries equation with a special source ⋮ Complex and coupled complex negative order AKNS equation ⋮ Negative-order KdV and negative-order KP equations: multiple soliton solutions ⋮ The integrable Vakhnenko-Parkes (VP) and the modified Vakhnenko-parkes (MVP) equations: multiple real and complex soliton solutions ⋮ Hierarchy of negative order equation and its Lax pair ⋮ Unnamed Item ⋮ Negative Kadomtsev-Petviashvili equation and extension of the sinh-Gordon equation ⋮ Multiple complex soliton solutions for integrable negative-order KdV and integrable negative-order modified KdV equations ⋮ Lax pairs, infinite conservation laws, Darboux transformation, bilinear forms and solitonic interactions for a combined Calogero-Bogoyavlenskii-Schiff-type equation ⋮ New interaction solutions and nonlocal symmetry of an equation combining the modified Calogero–Bogoyavlenskii–Schiff equation with its negative-order form ⋮ \(N\)-th Bäcklund transformation and soliton-cnoidal wave interaction solution to the combined KdV-negative-order KdV equation ⋮ Localized excitations with periodic and chaotic behaviors in \((1+1)\)-dimensional Korteweg-de Vries type system ⋮ Bäcklund transformation and CRE solvability for the negative-order modified KdV equation ⋮ On \((2+1)\)-dimensional mixed AKNS hierarchy ⋮ Peakon, compacton and loop excitations with periodic behavior in KdV type models related to Schrödinger system ⋮ Negative order MKdV hierarchy and a new integrable Neumann-like system ⋮ Nonlocal symmetry and Bäcklund transformation of a negative-order Korteweg-de Vries equation ⋮ Solutions with separated variables and breather structures in the \((1+1)\)-dimensional nonlinear systems ⋮ Quasiperiodic solutions of the negative-order Korteweg-de Vries hierarchy ⋮ Negative-order modified KdV equations: multiple soliton and multiple singular soliton solutions ⋮ Nonlocal symmetries of the KdV equation ⋮ Negative-order integrable modified KdV equations of higher orders ⋮ Generalized negative flows in hierarchies of integrable evolution equations ⋮ Soliton solutions for a negative order non-isospectral AKNS equation ⋮ NEW TYPES OF INTERACTIONS BASED ON VARIABLE SEPARATION SOLUTIONS VIA THE GENERAL PROJECTIVE RICCATI EQUATION METHOD ⋮ Hierarchy of lower Korteweg–de Vries equations and supersymmetry structure of Miura transformations ⋮ Reciprocal transformations of generalized negative flows in integrable hierarchies

Cites Work

This page was built for publication: Negative powers of Olver recursion operators