The binary Darboux transformation revisited and KdV solitons on arbitrary short‐range backgrounds

DOI10.1111/sapm.12436zbMath1529.35450OpenAlexW3195730096MaRDI QIDQ6085646

Alexei Rybkin

Publication date: 12 December 2023

Published in: Studies in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1111/sapm.12436

zbMATH Keywords

inverse scattering transformRiemann-Hilbert problemKdV equationbinary Darboux transformationdouble commutation method

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) KdV equations (Korteweg-de Vries equations) (35Q53) NLS equations (nonlinear Schrödinger equations) (35Q55) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35) Riemann-Hilbert problems in context of PDEs (35Q15) Soliton solutions (35C08)

Related Items (1)

Norming constants of embedded bound states and bounded positon solutions of the Korteweg-de Vries equation

Cites Work

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• Applications of a commutation formula
• A complete spectral characterization of the double commutation method
• Spectral deformations of one-dimensional Schrödinger operators
• Hamiltonian systems and Sturm-Liouville equations: Darboux transformation and applications
• Extreme superposition: rogue waves of infinite order and the Painlevé-III hierarchy
• Riemann-Hilbert problem for Camassa-Holm equation with step-like initial data
• Darboux transformations in integrable systems. Theory and their applications to geometry
• Riemann–Hilbert Problems, Their Numerical Solution, and the Computation of Nonlinear Special Functions
• Darboux transformation and multi-dark soliton forN-component nonlinear Schrödinger equations
• On the determination of a differential equation from its spectral function
• Commutation Methods Applied to the mKdV-Equation
• Algebraic construction of the Darboux matrix revisited
• Inverse scattering on the line
• Method for Solving the Korteweg-deVries Equation
• The Riemann–Hilbert Problem and Inverse Scattering
• (m)KdV solitons on the background of quasi-periodic finite-gap solutions
• On the double commutation method
• On classical solutions of the KdV equation
• On the Long-Time Asymptotic Behavior of the Modified Korteweg--de Vries Equation with Step-like Initial Data
• A Robust Inverse Scattering Transform for the Focusing Nonlinear Schrödinger Equation
• The effect of a positive bound state on the KdV solution: a case study ^*

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