The extended Fan's sub-equation method and its application to KdV-MKdV, BKK and variant Boussinesq equations
From MaRDI portal
Publication:2478723
DOI10.1016/j.physleta.2005.01.027zbMath1136.35451OpenAlexW2134248747MaRDI QIDQ2478723
Publication date: 25 March 2008
Published in: Physics Letters. A (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.physleta.2005.01.027
Related Items
Elliptic equation's new solutions and their applications to two nonlinear partial differential equations ⋮ A generalized algebraic method of new explicit and exact solutions of the nonlinear dispersive generalized Benjamin-Bona-Mahony equations ⋮ New exact traveling wave solutions for the modified form of Degasperis-Procesi equation ⋮ The extended \(\left( \frac {G^{\prime}}{G}\right)\)-expansion method and its applications to the Whitham-Broer-Kaup-like equations and coupled Hirota-Satsuma KdV equations ⋮ A sub-ODE method for finding exact solutions of a generalized KdV-mKdV equation with high-order nonlinear terms ⋮ Construction of solitonary and periodic solutions to some nonlinear equations using EXP-function method ⋮ Further improved extended Fan sub-equation method and new exact solutions of the (2 + 1)-dimensional Broer-Kaup-Kupershmidt equations ⋮ The periodic solutions to Kawahara equation by means of the auxiliary equation with a sixth-degree nonlinear term ⋮ On soliton solutions for the Fitzhugh-Nagumo equation with time-dependent coefficients ⋮ Lie symmetry analysis and new exact solutions for a higher-dimensional shallow water wave equation ⋮ Application of the rational (G' /G)-expansion method for solving some coupled and combined wave equations ⋮ Exact solutions for some nonlinear systems of partial differential equations ⋮ Sub-ODE method and solitary wave solutions for higher order nonlinear Schrödinger equation ⋮ A new auxiliary equation method for finding travelling wave solutions to KdV equation ⋮ Extended Jacobi elliptic function expansion solutions of variant Boussinesq equations ⋮ Auxiliary equation method for the mKdV equation with variable coefficients ⋮ Some new and general solutions to the compound KdV-Burgers system with nonlinear terms of any order ⋮ Construction of periodic and solitary wave solutions by the extended Jacobi elliptic function expansion method ⋮ Symmetry reductions, generalized solutions and dynamics of wave profiles for the \((2+1)\)-dimensional system of Broer-Kaup-Kupershmidt (BKK) equations ⋮ Application of the bifurcation method to the Whitham-Broer-Kaup-like equations ⋮ Regarding the shallow water in an ocean via a Whitham-Broer-Kaup-like system: hetero-Bäcklund transformations, bilinear forms and \(M\) solitons ⋮ New traveling wave solutions for nonlinear evolution equations ⋮ New families of travelling wave solutions for Boussinesq-Burgers equation and \((3+1)\)-dimensional Kadomtsev-Petviashvili equation ⋮ Thinking about the oceanic shallow water via a generalized Whitham-Broer-Kaup-Boussinesq-Kupershmidt system ⋮ Trigonometric function periodic wave solutions and their limit forms for the KdV-like and the PC-like equations ⋮ Exact travelling wave solutions for isothermal magnetostatic atmospheres by Fan subequation method ⋮ New exact solutions for the \((2+1)\)-dimensional Broer-Kaup-Kupershmidt equations ⋮ Double-Parameter Solutions of Projective Riccati Equations and Their Applications ⋮ Long-range interactions in \(\alpha \)-helical proteins with interspine coupling: modulational instability and exact soliton solutions ⋮ Symbolic computation of some new nonlinear partial differential equations of nanobiosciences using modified extended tanh-function method ⋮ N-solitons and cuspon waves solutions of \((2 + 1)\)-dimensional Broer-Kaup-Kupershmidt equations via hidden symmetries of Lie optimal system ⋮ Solitons and other solutions of \((3+1)\)-dimensional space-time fractional modified KdV-Zakharov-Kuznetsov equation ⋮ Construction of rogue waves and conservation laws of the complex coupled Kadomtsev–Petviashvili equation ⋮ Bifurcation of traveling wave solutions for the BBM-like \(B(2, 2)\) equation ⋮ Exact traveling wave solutions for a generalized Hirota-Satsuma coupled KdV equation by Fan sub-equation method ⋮ Searching for traveling wave solutions of nonlinear evolution equations in mathematical physics ⋮ Multiple soliton solutions for a new generalization of the associated Camassa-Holm equation by exp-function method ⋮ Exact solutions for \((4 + 1)\)-dimensional nonlinear Fokas equation using extended \(F\)-expansion method and its variant ⋮ A further improved extended Fan sub-equation method for \((2+1)\)-dimensional breaking soliton equations ⋮ Bifurcation and solitary-like solutions for compound KdV-Burgers-type equation ⋮ Solitary solutions, periodic solutions and compacton-like solutions using the Exp-function method ⋮ A new auxiliary function method for solving the generalized coupled Hirota-Satsuma KdV system ⋮ Coupled fractional nonlinear differential equations and exact Jacobian elliptic solutions for exciton-phonon dynamics ⋮ Modulation instability analysis, optical and other solutions to the modified nonlinear Schrödinger equation ⋮ The extended first kind elliptic sub-equation method and its application to the generalized reaction Duffing model ⋮ New exact travelling wave solutions of two nonlinear physical models ⋮ New exact travelling wave solutions for some nonlinear evolution equations. II ⋮ The extended Fan sub-equation method and its applications for a class of nonlinear evolution equations ⋮ Modulational instability and exact solutions for a three-component system of vector nonlinear Schrödinger equations ⋮ Exp-function method and its application to nonlinear equations ⋮ New exact travelling wave solutions of the generalized Zakharov equations ⋮ A unified lattice Boltzmann model for some nonlinear partial differential equations ⋮ New explicit travelling wave solutions of nonlinearly dispersive Boussinesq equations ⋮ Exact travelling wave solutions of nonlinear partial differential equations ⋮ Various exact solutions of nonlinear Schrödinger equation with two nonlinear terms ⋮ The compound \(\left(\frac{G'}{G}\right)\)-expansion method and double non-traveling wave solutions of \((2+1)\)-dimensional nonlinear partial differential equations ⋮ The modified extended Fan's subequation method and its application to \((2+1)\)-dimensional dispersive long wave equation ⋮ Exact solitary solutions of an inhomogeneous modified nonlinear Schrödinger equation with competing nonlinearities ⋮ The sub-ODE method for finding exact travelling wave solutions of generalized nonlinear Camassa-Holm, and generalized nonlinear Schrödinger equations ⋮ A generalized auxiliary equation method and its application to nonlinear Klein-Gordon and generalized nonlinear Camassa-Holm equations ⋮ The study of the solution to a generalized KdV-mKdV equation ⋮ Applications of the new compound Riccati equations rational expansion method and Fan's subequation method for the Davey-Stewartson equations ⋮ General exp\(_a\)-function method for nonlinear evolution equations ⋮ New exact travelling wave solutions of nonlinear evolution equation using a sub-equation ⋮ A note on exact complex travelling wave solutions for \((2+1)\)-dimensional B-type Kadomtsev-Petviashvili equation ⋮ Solitary-wave solutions to a dual equation of the Kaup-Boussinesq system ⋮ A reliable treatment for nonlinear Schrödinger equations ⋮ Application of the \((\frac{G'}{G})\)-expansion method for the complex KdV equation ⋮ New general solutions for the general elliptic and auxiliary equations and application to the coupled KdV equation ⋮ More solutions of the auxiliary equation to get the solutions for a class of nonlinear partial differential equations ⋮ New exact travelling waves solutions to the combined KdV-MKdV and generalized Zakharov equations ⋮ Travelling wave solutions for the generalized Burgers-Huxley equation ⋮ A further improved extended fan sub-equation method and its application to the \((3+1)\)-dimensional Kadomstev-Petviashvili equation ⋮ New exact solutions for a higher-order wave equation of KdV type using the multiple simplest equation method ⋮ Construction of Special Solutions for Nonintegrable Systems ⋮ Observations on the class of ``Balancing Principle for nonlinear PDEs that can be treated by the auxiliary equation method ⋮ The modified extended Fan sub-equation method and its application to the \((2+1)\)-dimensional Broer-Kaup-Kupershmidt equation
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- RATH: A Maple package for finding travelling solitary wave solutions to nonlinear evolution equations
- An automated \(\tanh\)-function method for finding solitary wave solutions to nonlinear evolution equations
- Exact solutions for some nonlinear partial differential equations
- Uniformly constructing a series of explicit exact solutions to nonlinear equations in mathematical physics
- A series of travelling wave solutions for two variant Boussinesq equations in shallow water waves
- Explicit exact solutions for compound KdV-type and compound KdV-Burgers-type equations with nonlinear terms of any order.
- Construction of new soliton-like solutions for the \((2+1)\) dimensional Kadomtsev-Petviashvili equation
- An algebraic method exactly solving two high-dimensional nonlinear evolution equations
- A series of new soliton-like solutions and double-like periodic solutions of a \((2 + 1)\)-dimensional dispersive long wave equation
- Exact travelling wave solutions of the Whitham-Broer-Kaup and Broer-Kaup-Kupershmidt equations
- A generalized method and general form solutions to the Whitham-Broer-Kaup equation
- Symbolic computation in nonlinear evolution equation: application to \((3+1)\)-dimensional Kadomtsev-Petviashvili equation
- Periodic wave solutions to a coupled KdV equations with variable coefficients
- Auxiliary equation method for solving nonlinear partial differential equations
- Construction of new soliton-like solutions of the (2 + 1) dimensional dispersive long wave equation
- Nonlinear transform and Jacobi elliptic function solutions of nonlinear equations
- Construction of new soliton-like solutions for the (2 + 1) dimensional KdV equation with variable coefficients
- On exact solutions of the coupled Klein--Gordon--Schrödinger and the complex coupled KdV equations using mapping method
- The periodic wave solutions and solitary wave solutions for a class of nonlinear partial differential equations
- New exact solutions of a new \((2+1)\)-dimensional integrable system
- Extended tanh-function method and its applications to nonlinear equations
- Simple Derivation of Backlund Transformation from Riccati Form of Inverse Method
- Relationships among Inverse Method, Backlund Transformation and an Infinite Number of Conservation Laws
- Wave Propagation in Nonlinear Lattice. I
- Exact Solution of the Korteweg—de Vries Equation for Multiple Collisions of Solitons
- Exact solutions to the combined KdV and mKdV equation
- Infinitely many Lax pairs and symmetry constraints of the KP equation
- delta -dressing and exact solutions for the (2+1)-dimensional Harry Dym equation
- Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations
