On the initial value problem for a class of nonlinear integral evolution equations including the sine–Hilbert equation

DOI10.1063/1.527763zbMath0637.45007OpenAlexW1979975167MaRDI QIDQ3778466

Mark J. Ablowitz, Paolo Maria Santíni, Athanassios S. Fokas

Publication date: 1987

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

Full work available at URL: https://doi.org/10.1063/1.527763

zbMATH Keywords

scatteringHilbert transformspectrummatrix Riemann-Hilbert problemsine-Hilbert equationnonlinear singular integral evolution equations

Mathematics Subject Classification ID

Integro-partial differential equations (45K05) Quantum scattering theory (81U99) Singular nonlinear integral equations (45G05)

Related Items (3)

Dynamics of solitons in a damped sine-Hilbert equation ⋮ Multiphase solutions and their reductions for a nonlocal nonlinear Schrödinger equation with focusing nonlinearity ⋮ The additional symmetries for the BTL and CTL hierarchies

Cites Work

• Algebraic Solitary Waves in Stratified Fluids
• On the limit from the intermediate long wave equation to the Benjamin–Ono 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 for the Benjamin‐Ono Equation—A Pivot to Multidimensional Problems
• Internal waves of permanent form in fluids of great depth

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