Extended double Wronskian solutions to the Whitham-Broer-Kaup equations in shallow water

DOI10.1007/s11071-010-9857-5zbMath1284.35344OpenAlexW2039412993MaRDI QIDQ395199

De-Xin Meng, Yi-Tian Gao, Xiao-Ling Gai, Guo-Dong Lin

Publication date: 29 January 2014

Published in: Nonlinear Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11071-010-9857-5

zbMATH Keywords

symbolic computationsolitonsrational solutionsbilinear formLax paircomplexitonsWhitham-Broer-Kaup equations in shallow waterWronskian technique

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) PDEs in connection with fluid mechanics (35Q35) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Soliton equations (35Q51) Soliton solutions (35C08) Trigonometric solutions to PDEs (35C09)

Related Items (7)

Rational and complexiton solutions of the \((3+1)\)-dimensional KP equation ⋮ Elastic and inelastic interactions of solitons for a variable-coefficient generalized dispersive water-wave system ⋮ Lax pair, infinitely-many conservation laws and soliton solutions for a set of the time-dependent Whitham-Broer-Kaup equations for the shallow water ⋮ Fully resonant soliton interactions in the Whitham-Broer-Kaup system based on the double Wronskian solutions ⋮ Bright soliton solutions and collisions for a \((3+1)\)-dimensional coupled nonlinear Schrödinger system in optical-fiber communication ⋮ Numerical solution of dispersive optical solitons with Schrödinger-Hirota equation by improved Adomian decomposition method ⋮ New Double Wronskian Solutions of the Whitham-Broer-Kaup System: Asymptotic Analysis and Resonant Soliton Interactions

Cites Work

• Unnamed Item
• Unnamed Item
• Transformations for a generalized variable-coefficient Korteweg-de Vries model from blood vessels, Bose-Einstein condensates, rods and positons with symbolic computation
• A generalized method and general form solutions to the Whitham-Broer-Kaup equation
• Multiple Riccati equations rational expansion method and complexiton solutions of the Whitham-Broer-Kaup equation
• Comment on: ``Spherical Kadomtsev-Petviashvili equation and nebulons for dust ion-acoustic waves with symbolic computation
• New double Wronskian solutions of the AKNS equation
• Bifurcation method and traveling wave solution to Whitham-Broer-Kaup equation
• Mathematics of dispersive water waves
• Similarity and conditional similarity reductions of a (2+1)-dimensional KdV equation via a direct method
• A Higher-Order Water-Wave Equation and the Method for Solving It
• Wave Propagation in Nonlinear Lattice. I
• Novel Wronskian Solutions to Boussinesq Equation
• Solitons and rational solutions of nonlinear evolution equations
• Inelastic interactions and double Wronskian solutions for the Whitham–Broer–Kaup model in shallow water
• Lax pair and Darboux transformation for multi-component modified Korteweg–de Vries equations
• THE DOUBLE WRONSKIAN SOLUTIONS TO THE KADOMTSET–PETVIASHVILI EQUATION
• BrightN-soliton solutions in terms of the triple Wronskian for the coupled nonlinear Schrödinger equations in optical fibers
• Soliton solutions of the Korteweg de Vries and the Kadomtsev-Petviashvili equations: the Wronskian technique
• Approximate equations for long water waves
• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
• Negatons, positons, rational-like solutions and conservation laws of the Korteweg–de Vries equation with loss and non-uniformity terms
• The Hirota-Satsuma Coupled KdV Equation and a Coupled Ito System Revisited
• Solving the Korteweg-de Vries equation by its bilinear form: Wronskian solutions
• delta -dressing and exact solutions for the (2+1)-dimensional Harry Dym equation
• A Computational Approach to the New Type Solutions of Whitham–Broer–Kaup Equation in Shallow Water
• Variational methods and applications to water waves

This page was built for publication: Extended double Wronskian solutions to the Whitham-Broer-Kaup equations in shallow water