\(N\)-soliton solutions for shallow water waves equations in \((1+1)\) and \((2+1)\) dimensions
From MaRDI portal
Publication:546064
DOI10.1016/J.AMC.2011.03.048zbMath1333.35244OpenAlexW2065870725MaRDI QIDQ546064
Publication date: 24 June 2011
Published in: Applied Mathematics and Computation (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.amc.2011.03.048
KdV equations (Korteweg-de Vries equations) (35Q53) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Soliton solutions (35C08)
Related Items (11)
Analytical non-autonomous wave solitons for the dispersive cubic-quintic Gross-Pitaevskii equation and the interactions ⋮ Multiple soliton solutions, soliton-type solutions and hyperbolic solutions for the Benjamin-Bona-Mahony equation with variable coefficients in rotating fluids and one-dimensional transmitted waves ⋮ Three-dimensional exact solutions of Gross-Pitaevskii equation with variable coefficients ⋮ CRE solvability and soliton-cnoidal wave interaction solutions of the dissipative \((2+1)\)-dimensional AKNS equation ⋮ Solving the \((3+1)\)-dimensional generalized KP and BKP equations by the multiple exp-function algorithm ⋮ Dynamical analysis of diversity lump solutions to the (2+1)-dimensional dissipative Ablowitz–Kaup–Newell–Segure equation ⋮ The periodic wave solutions for a \((2+1)\)-dimensional \textit{AKNS} equation ⋮ Multiple soliton solutions and fusion interaction phenomena for the \((2 + 1)\)-dimensional modified dispersive water-wave system ⋮ Darboux transformation and conservation laws of a integrable evolution equations with \(3 \times 3\) Lax pairs ⋮ Non-autonomous wave solutions for the Gross-Pitaevskii (GP) equation with a parabola external potential in Bose-Einstein condensates ⋮ Variational multiscale element-free Galerkin method combined with the moving Kriging interpolation for solving some partial differential equations with discontinuous solutions
Cites Work
- Unnamed Item
- New traveling wave solutions to AKNS and SKdV equations
- The tanh-coth and the sech methods for exact solutions of the Jaulent-Miodek equation
- Symbolic methods to construct exact solutions of nonlinear partial differential equations
- Exact travelling wave solutions for the dissipative \((2+1)\)-dimensional AKNS equation
- Bilinear transformation method
- The extended tanh method for new solitons solutions for many forms of the fifth-order KdV equations
- Solitary wave solutions of the generalized shallow water wave (GSWW) equation by Hirota's method, tanh-coth method and exp-function method
- The Hirota's direct method for multiple-soliton solutions for three model equations of shallow water waves
- Compactons dispersive structures for variants of the \(K(n,n)\) and the KP equations
- The tanh method for traveling wave solutions of nonlinear equations
- The tanh-coth method for solitons and kink solutions for nonlinear parabolic equations
- Multiple-soliton solutions for the KP equation by Hirota's bilinear method and by the tanh-coth method
- Multiple-front solutions for the Burgers equation and the coupled Burgers equations
- The tanh-coth and the sine-cosine methods for kinks, solitons, and periodic solutions for the Pochhammer-Chree equations
- Multiple soliton solutions for the \((2+1)\)-dimensional asymmetric Nizhnik-Novikov-Veselov equation
- Traveling-wave solutions of the Schwarz-Korteweg-de Vries equation in \(2+1\) dimensions and the Ablowitz-Kaup-Newell-Segur equation through symmetry reductions
- N-Soliton Solutions of Model Equations for Shallow Water Waves
- Exact Solution of the Korteweg—de Vries Equation for Multiple Collisions of Solitons
- Integrable (2+1)-dimensional and (3+1)-dimensional breaking soliton equations
- A search for bilinear equations passing Hirota’s three-soliton condition. I. KdV-type bilinear equations
- A search for bilinear equations passing Hirota’s three-soliton condition. II. mKdV-type bilinear equations
- The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
- On a shallow water wave equation
- Unified approach to Miura, Bäcklund and Darboux Transformations for Nonlinear Partial Differential Equations
- New solitary-wave special solutions with compact support for the nonlinear dispersive \(K(m,n)\) equations
This page was built for publication: \(N\)-soliton solutions for shallow water waves equations in \((1+1)\) and \((2+1)\) dimensions