The singular solutions of a nonlinear evolution equation taking continuous part of the spectral data into account in inverse scattering method

DOI10.1016/j.chaos.2012.02.019zbMath1267.35149OpenAlexW2139695441MaRDI QIDQ1952545

E. John Parkes, Vyacheslav O. Vakhnenko

Publication date: 31 May 2013

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.chaos.2012.02.019

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) Soliton solutions (35C08)

Related Items (8)

The Ostrovsky-Vakhnenko equation: A Riemann-Hilbert approach ⋮ Dynamical behavior of traveling wave solutions for a \((2+1)\)-dimensional Bogoyavlenskii coupled system ⋮ The inverse problem for some special spectral data ⋮ Explicit quasi-periodic solutions of the Vakhnenko equation ⋮ Approach in theory of nonlinear evolution equations: the Vakhnenko-Parkes equation ⋮ Four-component integrable systems inspired by the Toda and the Davydov-Kyslukha models ⋮ Application of the ITEM for solving three nonlinear evolution equations arising in fluid mechanics ⋮ Integrability of the modified generalised Vakhnenko equation

Cites Work

• Comment on ``Application of (\(G'/G\))-expansion method to travelling-wave solutions of three nonlinear evolution equation
• Application of (\(\frac{G'}{G}\))-expansion method to travelling wave solutions of three nonlinear evolution equation
• A note on ``New travelling wave solutions to the Ostrovsky equation
• The inverse problem for a general \(n \times n\) spectral equation
• Reciprocal transformations for a spectral problem in \(2+1\) dimensions
• Bäcklund transformations, the inverse scattering method, solitons, and their applications. NSF research workshop on contact transformations
• The calculation of multi-soliton solutions of the Vakhnenko equation by the inverse scattering method.
• The tanh and the sine-cosine methods for exact solutions of the MBBM and the Vakhnenko equations
• N-soliton solutions for the Vakhnenko equation and its generalized forms
• On the Inverse Scattering Problem for Cubic Eigenvalue Problems of the Class ψ_xxx + 6Qψ_x + 6R_ψ = λψ
• Solitons in a nonlinear model medium
• The inverse scattering transform: Semi-infinite interval
• The two loop soliton solution of the Vakhnenko equation
• The stability of solutions of Vakhnenko's equation
• High-frequency soliton-like waves in a relaxing medium
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