A note on the \(G'/G\)-expansion method

DOI10.1016/j.amc.2010.03.071zbMath1203.35228OpenAlexW1695086337MaRDI QIDQ609338

Publication date: 30 November 2010

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2010.03.071

zbMATH Keywords

exact solution general solution nonlinear evolution equation traveling wave \(G^{\prime}/G\)-expansion method tanh-method

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Soliton equations (35Q51) Traveling wave solutions (35C07) Soliton solutions (35C08) Methods of ordinary differential equations applied to PDEs (35A24)

Related Items

On wave structures described by the generalized Kuramoto-Sivashinsky equation, New exact solutions for the Kaup-Kupershmidt equation, Solitons and other exact solutions for two nonlinear PDEs in mathematical physics using the generalized projective Riccati equations method, Kink solitary solutions to generalized Riccati equations with polynomial coefficients, On traveling waves in lattices: the case of Riccati lattices, Analytical properties and exact solutions of the Lotka-Volterra competition system, Painlevé analysis and exact solutions for the Belousov-Zhabotinskii reaction-diffusion system, Higher order solitary solutions to the meta-model of diffusively coupled Lotka-Volterra systems, Comment on ``Application of (\(G'/G\))-expansion method to travelling-wave solutions of three nonlinear evolution equation, A new variable-coefficient Riccati subequation method for solving nonlinear lattice equations, Scattering and intrinsic irreversibility, A landscape of time asymmetry, A note on ``New travelling wave solutions to the Ostrovsky equation, Traveling wave solutions to Kawahara and related equations, Exact solutions and optical soliton solutions for the nonlinear Schrödinger equation with fourth-order dispersion and cubic-quintic nonlinearity, A note on the \(\exp (-\varphi (z))\) expansion method, Some exact solutions for Toda type lattice differential equations using the improved (G′/G)-expansion method, On solutions of the fifth-order dispersive equations with porous medium type non-linearity, From the Fermi-Pasta-Ulam model to higher-order nonlinear evolution equations, Efficient analytical algorithms to study Fokas dynamical models involving M-truncated derivative, Painlevé analysis and exact solutions of the fourth-order equation for description of nonlinear waves, Comment on: ``The (G\(^{\prime}\)/G)-expansion method for the nonlinear lattice equations, Exact solutions of damped improved Boussinesq equations by extended \((G'/G)\)-expansion method, Traveling wave reduction of the modified KdV hierarchy: the Lax pair and the first integrals, The two-variable \((G'/G, 1/G)\)-expansion method for solving the nonlinear KdV-mKdV equation, Nonlinear differential equations of the second, third and fourth order with exact solutions, The \((G'/ G, 1 / G)\)-expansion method and its applications to find the exact solutions of nonlinear PDEs for nanobiosciences, The \((G' / G, 1 / G)\)-expansion method and its applications for solving two higher order nonlinear evolution equations, Quasi-exact solutions of the dissipative Kuramoto-Sivashinsky equation, Polynomials in logistic function and solitary waves of nonlinear differential equations, The effect of perturbed advection on a class of solutions of a non-linear reaction-diffusion equation, Painlevé analysis and exact solutions for the modified Korteweg-de Vries equation with polynomial source, Exact solutions and integrability of the Duffing-van der Pol equation, On solutions of generalized modified Korteweg-de Vries equation of the fifth order with dissipation, A new Jacobi elliptic function expansion method for solving a nonlinear PDE describing the nonlinear low-pass electrical lines, Quasi-exact solutions of nonlinear differential equations, Refinement of the Korteweg-de Vries equation from the Fermi-pasta-Ulam model, Traveling wave solutions of the nonlinear \((3 + 1)\)-dimensional Kadomtsev-Petviashvili equation using the two variables \((G/G, 1/G)\)-expansion method, Exact solutions of the equation for surface waves in a convecting fluid, Improved \((G'/G)\)-expansion method for the space and time fractional foam drainage and KdV equations, A note on the (\(G^{\prime }/G\))-expansion method again, Logistic function as solution of many nonlinear differential equations, On nonlinear differential equation with exact solutions having various pole orders, Analytical solutions of the Lorenz system, Painlevé analysis and a solution to the traveling wave reduction of the Radhakrishnan-Kundu-Lakshmanan equation, Generalization of the simplest equation method for nonlinear non-autonomous differential equations, A study on the (2+1)-dimensional first extended Calogero-Bogoyavlenskii-Schiff equation, Painlevé analysis and exact solutions of a predator–prey system with diffusion, Painlevé analysis and exact solutions of the Korteweg-de Vries equation with a source, A note on solutions of the generalized Fisher equation

Uses Software

ATFM

Cites Work