Integrable potentials by Darboux transformations in rings and quantum and classical problems

DOI10.1134/S0040577918100069OpenAlexW2899629435MaRDI QIDQ1716181

Erdal Karapınar

Publication date: 4 February 2019

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0040577918100069

zbMATH Keywords

Burgers equationDarboux transformationchain in a ringDarboux-Matveev transformationdressing the Dicke Hamiltonianfactoring a polynomial differential operatorgeneralized Miura transformation

Mathematics Subject Classification ID

Hamilton's equations (70H05) General theory of partial differential operators (47F05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems (70S05)

Cites Work

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• Darboux transformation and explicit solutions of the Kadomtsev-Petviashvili equation, depending on functional parameters
• A dressing method in mathematical physics.
• Dressing method in matter+radiation quantum models
• Multi-rogue waves solutions: from the NLS to the KP-I equation
• Division of differential operators, intertwine relations and Darboux transformations.

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