Approach in theory of nonlinear evolution equations: the Vakhnenko-Parkes equation

DOI10.1155/2016/2916582zbMath1455.35217OpenAlexW2300553681WikidataQ59122205 ScholiaQ59122205MaRDI QIDQ1796539

Vyacheslav O. Vakhnenko, E. John Parkes

Publication date: 17 October 2018

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

Full work available at URL: https://doi.org/10.1155/2016/2916582

zbMATH Keywords

inverse scattering transformBäcklund transformationsoliton solutionVakhnenko equation

Mathematics Subject Classification ID

Soliton equations (35Q51) 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) Soliton solutions (35C08)

Related Items (5)

Various forms of lumps and interaction solutions to generalized Vakhnenko Parkes equation arising from high-frequency wave propagation in electromagnetic physics ⋮ Propagation of traveling wave solutions to the Vakhnenko-Parkes dynamical equation via modified mathematical methods ⋮ Interaction dynamics of hybrid solitons and breathers for extended generalization of Vakhnenko equation ⋮ The integrable Vakhnenko-Parkes (VP) and the modified Vakhnenko-parkes (MVP) equations: multiple real and complex soliton solutions ⋮ Loop-like kink breather and its transition phenomena for the Vakhnenko equation arising from high-frequency wave propagation in electromagnetic physics

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
• Hamiltonian methods in the theory of solitons. Transl. from the Russian by A. G. Reyman
• Stability of envelope waves
• The inverse problem for a general \(n \times n\) spectral equation
• Partial differential equations and solitary waves theory
• 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
• On laminar steady flow of gas mixtures in pipes and channels
• A Bäcklund transformation and the inverse scattering transform method for the generalised Vakhnenko equation
• The \(N\)-soliton solution of the modified generalised Vakhnenko equation (a new nonlinear evolution equation).
• The calculation of multi-soliton solutions of the Vakhnenko equation by the inverse scattering method.
• Periodic and solitary-wave solutions of the Degasperis-Procesi equation
• Symmetry reductions and exact solutions of shallow water wave equations
• The singular solutions of a nonlinear evolution equation taking continuous part of the spectral data into account in inverse scattering method
• The tanh and the sine-cosine methods for exact solutions of the MBBM and the Vakhnenko equations
• The N -soliton solution of a generalised Vakhnenko equation
• Hirota's Bilinear Method and its Generalization
• The Modified Korteweg-de Vries Equation
• N-Soliton Solutions of Model Equations for Shallow Water Waves
• A Bäcklund Transformation for a Higher Order Korteweg-De Vries Equation
• An Extension of Nonlinear Evolution Equations of the K-dV (mK-dV) Type to Higher Orders
• Special singularity function for continuous part of the spectral data in the associated eigenvalue problem for nonlinear equations
• Solutions Associated with Discrete and Continuous Spectrums in the Inverse Scattering Method for the Vakhnenko-Parkes Equation
• N-soliton solutions for the Vakhnenko equation and its generalized forms
• Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States
• A search for integrable bilinear equations: The Painlevé approach
• Algorithmic method for deriving Lax pairs from the invariant Painlevé analysis of nonlinear partial differential equations
• A New Form of Backlund Transformations and Its Relation to the Inverse Scattering Problem
• Method for Solving the Korteweg-deVries Equation
• On the Structure During Interaction of the Two-Soliton Solution of the Korteweg–de Vries Equation
• The two-dimensional stability of periodic and solitary wave trains on a water surface over arbitrary depth
• A search for bilinear equations passing Hirota’s three-soliton condition. I. KdV-type bilinear equations
• Soliton and antisoliton resonant interactions
• On the Inverse Scattering Problem for Cubic Eigenvalue Problems of the Class ψ_xxx + 6Qψ_x + 6R_ψ = λψ
• Inverse scattering and the boussinesq equation
• Solitons in a nonlinear model medium
• Solitons on moving space curves
• The two loop soliton solution of the Vakhnenko equation
• The stability of solutions of Vakhnenko's equation
• On the Toda Lattice. II: Inverse-Scattering Solution
• High-frequency soliton-like waves in a relaxing medium
• Korteweg-de Vries Equation and Generalizations. III. Derivation of the Korteweg-de Vries Equation and Burgers Equation
• Prolongation algebras and Hamiltonian operators for peakon equations
• The Ostrovsky–Vakhnenko equation by a Riemann–Hilbert approach
• A Riemann–Hilbert approach for the Degasperis–Procesi equation
• Expansion in eigenfunctions of non-self-adjoint singular differential operators of second order
• Integrals of nonlinear equations of evolution and solitary waves
• A soliton on a vortex filament
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Approach in theory of nonlinear evolution equations: the Vakhnenko-Parkes equation