The initial-boundary value problem for the Ostrovsky-Vakhnenko equation on the half-line

DOI10.1007/s11040-016-9223-zzbMath1413.35365arXiv1609.08207OpenAlexW2526711037MaRDI QIDQ1663431

Jian Xu, En-gui Fan

Publication date: 21 August 2018

Published in: Mathematical Physics, Analysis and Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1609.08207

zbMATH Keywords

initial-boundary value problemRiemann-Hilbert problemOstrovsky-Vakhnenko equation

Mathematics Subject Classification ID

Boundary value problems in the complex plane (30E25) Riemann-Hilbert problems in context of PDEs (35Q15) Boundary value and inverse problems for harmonic functions in higher dimensions (31B20)

Related Items

Initial-boundary value problems of the coupled modified Korteweg–de Vries equation on the half-line via the Fokas method ⋮ Initial-Boundary Value Problem for Two-Component Gerdjikov–Ivanov Equation with 3 × 3 Lax Pair on Half-Line ⋮ An initial-boundary value problem for the integrable spin-1 Gross-Pitaevskii equations with a 4 × 4 Lax pair on the half-line ⋮ Initial-boundary value problem for the spin-1 Gross-Pitaevskii system with a 4 × 4 Lax pair on a finite interval ⋮ Initial-Boundary Value Problem for Integrable Nonlinear Evolution Equation with 3 × 3 Lax Pairs on the Interval ⋮ N-soliton solutions of the coupled Kundu equations based on the Riemann-Hilbert method ⋮ Prolongation structures and \(N\)-soliton solutions for a new nonlinear Schrödinger-type equation via Riemann-Hilbert approach

Cites Work

• Unnamed Item
• Global existence of small-norm solutions in the reduced Ostrovsky equation
• Initial-boundary value problems for integrable evolution equations with \(3\times 3\) Lax pairs
• Hamiltonian structures for the Ostrovsky-Vakhnenko equation
• Well-posedness and small data scattering for the generalized Ostrovsky equation
• The Degasperis-Procesi equation on the half-line
• Continuity properties of the solution map for the generalized reduced Ostrovsky equation
• On stationary solutions of the reduced Ostrovsky equation: periodic waves, compactons and compound solitons
• Local and global well-posedness for the Ostrovsky equation
• Cauchy problem for the Ostrovsky equation
• The three-wave equation on the half-line
• Integrable nonlinear evolution equations on the half-line
• Initial-value problem for coupled Boussinesq equations and a hierarchy of Ostrovsky equations
• Long-time asymptotics for the Degasperis-Procesi equation on the half-line
• Initial-Boundary Value Problem for Integrable Nonlinear Evolution Equation with 3 × 3 Lax Pairs on the Interval
• The unified transform method for the Sasa–Satsuma equation on the half-line
• A Unified Approach to Boundary Value Problems
• Solitons in a nonlinear model medium
• The stability of solutions of Vakhnenko's equation
• A unified transform method for solving linear and certain nonlinear PDEs
• High-frequency soliton-like waves in a relaxing medium
• Prolongation algebras and Hamiltonian operators for peakon equations
• The Ostrovsky–Vakhnenko equation by a Riemann–Hilbert approach
• Initial-boundary value problem for the two-component nonlinear Schrödinger equation on the half-line
• An integrable evolution equation for surface waves in deep water