Bäcklund transformations and soliton solutions for a \((2+1)\)-dimensional Korteweg-de Vries-type equation in water waves
DOI10.1007/s11071-015-2109-yzbMath1348.37108OpenAlexW763926763MaRDI QIDQ329146
Xi-Yang Xie, Bo Tian, Yu-Feng Wang, Ya Sun, Yun-Po Wang, Ming Wang
Publication date: 21 October 2016
Published in: Nonlinear Dynamics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s11071-015-2109-y
symbolic computationBäcklund transformationsBell polynomialswater waves\((2+1)\)-dimensional Korteweg-de Vries-type equationsoliton interactions
PDEs in connection with fluid mechanics (35Q35) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15)
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- Bell-polynomial construction of Bäcklund transformations with auxiliary independent variable for some soliton equations with one tau-function
- A study of shallow water waves with Gardner's equation
- Additional conservation laws for Rosenau-KdV-RLW equation with power law nonlinearity by Lie symmetry
- Linear superposition principle applying to Hirota bilinear equations
- Topological 1-soliton solution of the generalized KdV equation with generalized evolution
- Topological and non-topological solitons of the Klein-Gordon equations in \(1+2\) dimensions
- Exact solutions and Painlevé analysis of a new (2+1)-dimensional generalized KdV equation
- Adiabatic parameter dynamics of perturbed solitary waves
- Solitary waves of Boussinesq equation in a power law media
- Positon and positon-like solutions of the Korteweg-de Vries and sine-Gordon equations.
- Exact solutions of a KdV equation with variable coefficients via Exp-function method
- 1-soliton solution of the generalized KdV equation with generalized evolution
- Exact solutions of KdV equation with time-dependent coefficients
- 1-soliton solution of the \(K(m,n)\) equation with generalized evolution and time-dependent damping and dispersion
- 1-soliton solution of the coupled KdV equation and Gear-Grimshaw model
- Topological soliton solutions of \((2+1)\)-dimensional KdV equation with power law nonlinearity and time-dependent coefficients
- Exponential polynomials
- Bell-polynomial approach and soliton solutions for the Zhiber-Shabat equation and (2+1)-dimensional Gardner equation with symbolic computation
- Singular solitons, shock waves, and other solutions to potential KdV equation
- Solitary waves for power-law regularized long-wave equation and \(R(m,n)\) equation
- Solitary wave solution for KdV equation with power-law nonlinearity and time-dependent coefficients
- Elastic interactions between multi-valued foldons and anti-foldons for the \({(2+1)}\)-dimensional variable coefficient Broer-Kaup system in water waves
- Wave Propagation in Nonlinear Lattice. I
- A study on the (2 + 1)-dimensional KdV4 equation derived by using the KdV recursion operator
- 2 + 1 KdV(N) equations
- Soliton solutions for a generalized fifth-order KdV equation with t-dependent coefficients
- Solitons and other solutions of the long-short wave equation
- Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States
- On the combinatorics of the HirotaD-operators
- Method for Solving the Korteweg-deVries Equation
- A symbolic algorithm for computing recursion operators of nonlinear partial differential equations
- Symmetries and Integrability
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