Nonlinear evolution equations associated with a Riemann–Hilbert scattering problem

DOI10.1063/1.526760zbMath0581.35075OpenAlexW2029067389MaRDI QIDQ3704320

Mark J. Ablowitz, Paolo Maria Santíni, Antonio Degasperis

Publication date: 1985

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

Full work available at URL: https://doi.org/10.1063/1.526760

zbMATH Keywords

nonlinear evolution equationsN-soliton solutiondirect linearizationRiemann-Hilbert scattering problem

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) Nonlinear higher-order PDEs (35G20) Partial differential equations of mathematical physics and other areas of application (35Q99)

Related Items

Nonlocal evolution equations associated with the Zakharov-Shabat problem ⋮ Generalized intermediate long-wave hierarchy in zero-curvature representation with noncommutative spectral parameter ⋮ Dynamics of solitons in a damped sine-Hilbert equation ⋮ A spectral transform for the intermediate nonlinear Schrödinger equation ⋮ New integrable nonlinear integrodifferential equations and related solvable finite-dimensional dynamical systems ⋮ Nonlocal integrable equations from the mKP hierarchy ⋮ An application of the inverse scattering transform to the modified intermediate long wave equation ⋮ Invertible changes of variables generated by Bäcklund transformations

Cites Work

• Algebraic Solitary Waves in Stratified Fluids
• On the limit from the intermediate long wave equation to the Benjamin–Ono equation
• On a Bäcklund transformation and scattering problem for the modified intermediate long wave equation
• Direct and inverse scattering problems of the nonlinear intermediate long wave equation
• Multi-soliton solutions in a finite depth fluid
• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
• The Inverse Scattering Transform for the Benjamin‐Ono Equation—A Pivot to Multidimensional Problems
• Internal waves of permanent form in fluids of great depth