Integrability of the modified generalised Vakhnenko equation
From MaRDI portal
Publication:2872442
DOI10.1063/1.4764845zbMath1296.37049OpenAlexW2033329014MaRDI QIDQ2872442
Publication date: 14 January 2014
Published in: Journal of Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://semanticscholar.org/paper/c39b642db2015ab85290bf0a7429866691f268c3
Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Theta functions and abelian varieties (14K25) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35) Periodic and quasi-periodic flows and diffeomorphisms (37C55)
Related Items
The interactions of \(N\)-soliton solutions for the generalized (2+1)-dimensional variable-coefficient fifth-order KdV equation ⋮ Bell polynomials approach for two higher-order KdV-type equations in fluids ⋮ Bilinear Bäcklund transformations and explicit solutions of a \((3+1)\)-dimensional nonlinear equation ⋮ Bäcklund transformation and solutions of a \((3+1)\)-dimensional nonlinear evolution equation ⋮ Bäcklund transformation, infinite conservation laws and periodic wave solutions of a generalized (3+1)-dimensional nonlinear wave in liquid with gas bubbles ⋮ Integrability of and differential-algebraic structures for spatially 1D hydrodynamical systems of Riemann type ⋮ The differential-algebraic analysis of symplectic and Lax structures related with new Riemann-type hydrodynamic systems ⋮ Self-consistent sources and conservation laws for a super Broer-Kaup-Kupershmidt equation hierarchy ⋮ New interaction solutions for a (2 + 1)-dimensional Vakhnenko equation ⋮ Integrability of a (2+1)-dimensional generalized breaking soliton equation ⋮ Bell polynomials approach applied to \((2+1)\)-dimensional variable-coefficient Caudrey-Dodd-Gibbon-Kotera-Sawada equation ⋮ The rational solutions and quasi-periodic wave solutions as well as interactions of \(N\)-soliton solutions for \(3 + 1\) dimensional Jimbo-Miwa equation ⋮ Bell polynomial approach to an extended Korteweg–de Vries equation ⋮ Nonlocal symmetries of some nonlinear partial differential equations with third-order Lax pairs ⋮ N-soliton solutions of the coupled Kundu equations based on the Riemann-Hilbert method ⋮ Integrability and exact solutions of the (2+1)-dimensional KdV equation with Bell polynomials approach ⋮ A numerical study of \(N\)-periodic wave solutions to four integrable equations ⋮ On the integrability of the (1+1)‐dimensional and (2+1)‐dimensional Ito equations ⋮ Integrability for the generalised variable-coefficient fifth-order Korteweg-de Vries equation with Bell polynomials ⋮ Exact solutions and symmetry analysis of a Boussinesq type equation for longitudinal waves through a magneto-electro-elastic circular rod ⋮ Lax pair, conservation laws, and multi-shock wave solutions of the DJKM equation with Bell polynomials and symbolic computation
Cites Work
- Unnamed Item
- On the periodic solutions for both nonlinear differential and difference equations: a unified approach
- The integrability of nonisospectral and variable-coefficient KdV equation with binary Bell polynomials
- New exact solutions and Bäcklund transformation for Boiti-Leon-Manna-Pempinelli equation
- On a direct procedure for the quasi-periodic wave solutions of the supersymmetric Ito's equation
- Soliton multidimensional equations and integrable evolutions preserving Laplace's equation
- On stationary solutions of the reduced Ostrovsky equation: periodic waves, compactons and compound solitons
- Soliton equations and simple combinatorics
- Cusp and loop soliton solutions of short-wave models for the Camassa-Holm and Degasperis-Procesi equations
- The interaction processes of the \(N\)-soliton solutions for an extended generalization of Vakhnenko equation
- 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).
- On a direct procedure for the disclosure of Lax pairs and Bäcklund transformations
- The calculation of multi-soliton solutions of the Vakhnenko equation by the inverse scattering method.
- A series of new soliton-like solutions and double-like periodic solutions of a \((2 + 1)\)-dimensional dispersive long wave equation
- Exponential polynomials
- Combined Wronskian solutions to the 2D Toda molecule equation
- The singular solutions of a nonlinear evolution equation taking continuous part of the spectral data into account in inverse scattering method
- A unified rational expansion method to construct a series of explicit exact solutions to nonlinear evolution equations
- A new chaotic algorithm for image encryption
- Symmetry analysis and exact solutions of the 2+1 dimensional sine-Gordon system
- Binary Bell polynomials and Darboux covariant Lax pairs
- The N -soliton solution of a generalised Vakhnenko equation
- Relationships among Inverse Method, Backlund Transformation and an Infinite Number of Conservation Laws
- N-Soliton Solutions of Model Equations for Shallow Water Waves
- A Direct Method of Calculating Periodic Wave Solutions to Nonlinear Evolution Equations. I. Exact Two-Periodic Wave Solution
- A Direct Method of Calculating Periodic Wave Solutions to Nonlinear Evolution Equations. II. Exact One- and Two-Periodic Wave Solution of the Coupled Bilinear Equations
- Special singularity function for continuous part of the spectral data in the associated eigenvalue problem for nonlinear equations
- A Direct procedure on the Integrability of Nonisospectral and Variable-Coefficient MKdV Equation
- New Bilinear Bäcklund Transformation and Lax Pair for the Supersymmetric Two-Boson Equation
- Binary Bell polynomial approach to the non-isospectral and variable-coefficient KP equations
- Solutions Associated with Discrete and Continuous Spectrums in the Inverse Scattering Method for the Vakhnenko-Parkes Equation
- Binary Bell Polynomials Approach to Generalized Nizhnik—Novikov—Veselov Equation
- Binary Bell Polynomials, Bilinear Approach to Exact Periodic Wave Solutions of (2 + 1)-Dimensional Nonlinear Evolution Equations
- Bäcklund Transformations and Solutions of a Generalized Kadomtsev—Petviashvili Equation
- N-soliton solutions for the Vakhnenko equation and its generalized forms
- On the combinatorics of the HirotaD-operators
- EXACT ONE-PERIODIC AND TWO-PERIODIC WAVE SOLUTIONS TO HIROTA BILINEAR EQUATIONS IN (2+1) DIMENSIONS
- A modified KdV equation with self-consistent sources in non-uniform media and soliton dynamics
- A KIND OF EXPLICIT QUASI-PERIODIC SOLUTION AND ITS LIMIT FOR THE TODA LATTICE EQUATION
- Quasi-periodic waves and an asymptotic property for the asymmetrical Nizhnik–Novikov–Veselov equation
- Solitons in a nonlinear model medium
- The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
- The two loop soliton solution of the Vakhnenko equation
- Some new exact solutions of the Novikov - Veselov equation
- Inverse scattering transform for the KPI equation on the background of a one-line soliton*
- Construction of Bäcklund Transformations with Binary Bell Polynomials
- High-frequency soliton-like waves in a relaxing medium
- On a direct bilinearization method: Kaup's higher-order water wave equation as a modified nonlocal Boussinesq equation
- Abundant solitary wave structures of the nonlinear coupled scalar field equations
- Darboux covariant Lax pairs and infinite conservation laws of the (2+1)-dimensional breaking soliton equation
- Bell-polynomial approach and N-soliton solution for the extended Lotka–Volterra equation in plasmas
- Multiple Soliton-like and Periodic-like Solutions to the Generalization of Integrable (2+1)-Dimensional Dispersive Long-Wave Equations
