On the validity and reliability of the (\(G^{\prime}/G\))-expansion method by using higher-order nonlinear equations

DOI10.1016/j.amc.2009.01.075zbMath1162.65391OpenAlexW2139944064MaRDI QIDQ1021688

İsmail Aslan, Turgut Öziş

Publication date: 9 June 2009

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

Full work available at URL: http://hdl.handle.net/11147/2691

zbMATH Keywords

traveling wave solutionssolitary wave solutionssixth-order Boussinesq equation(\(G^{\prime}/G\))-expansion methodninth-order KdV equation

Mathematics Subject Classification ID

Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)

Related Items (31)

New application of \((G'/G)\)-expansion method for generalized (2+1)-dimensional nonlinear evolution equations ⋮ A new analysis of a partial differential equation arising in biology and population genetics via semi analytical techniques ⋮ Generalized solitary and periodic wave solutions to a \((2+1)\)-dimensional Zakharov-Kuznetsov equation ⋮ Observations on the basic \((G'/G)\)-expansion method for finding solutions to nonlinear evolution equations ⋮ Application of the \((\frac{G'}{G})\)-expansion method to \((3 +1)\)-dimensional nonlinear evolution equations ⋮ Some exact solutions for Toda type lattice differential equations using the improved (G′/G)-expansion method ⋮ The solitary waves, quasi-periodic waves and integrability of a generalized fifth-order Korteweg-de Vries equation ⋮ The \((\frac{G'}G)\)-expansion method for Tzitzéica type nonlinear evolution equations ⋮ Application of the \((\frac{G'}{G})\)-expansion method for the Zhiber-Shabat equation and other related equations ⋮ Using \(\left( \frac{G^{\prime}}{G} \right)\)-expansion method to seek the traveling wave solution of Kolmogorov-Petrovskii-Piskunov equation ⋮ Analytic investigation of the \((2+1)\)-dimensional Schwarzian Korteweg-de Vries equation for traveling wave solutions ⋮ \(N\)-fold Darboux transformation and solitonic interactions of a variable-coefficient generalized Boussinesq system in shallow water ⋮ Analytic solutions for generalized forms of the nonlinear heat conduction equation ⋮ The modified \(\frac {G \prime}{G}\)-expansion method and traveling wave solutions of nonlinear the perturbed nonlinear Schrödinger's equation with Kerr law nonlinearity ⋮ Application of \((\frac{G'}{G})\)-expansion method to regularized long wave (RLW) equation ⋮ Application of (\(\frac{G'}{G}\))-expansion method to travelling wave solutions of three nonlinear evolution equation ⋮ Hyperbolic and trigonometric solutions for some nonlinear evolution equations ⋮ Application of the Exp-function method to the (2+1)-dimensional Boiti–Leon–Pempinelli equation using symbolic computation ⋮ A direct method for constructing the traveling wave solutions of a modified generalized Vakhnenko equation ⋮ New exact solutions to the perturbed nonlinear Schrödinger's equation with Kerr law nonlinearity via modified trigonometric function series method ⋮ Bell-Polynomial Approach and Soliton Solutions for Some Higher-Order Korteweg-de Vries Equations in Fluid Mechanics, Plasma Physics and Lattice Dynamics ⋮ The \((\frac{G'}{G})\)-expansion method for some nonlinear evolution equations ⋮ New application of \((G'/G)\)-expansion method to a nonlinear evolution equation ⋮ Application of the \(G^{\prime}/G\)-expansion method to Kawahara type equations using symbolic computation ⋮ The Ablowitz-Ladik lattice system by means of the extended (\(G^{\prime}/G)\)-expansion method ⋮ The non-traveling wave solutions and novel fractal soliton for the \((2 + 1)\)-dimensional Broer-Kaup equations with variable coefficients ⋮ Exact and explicit solutions to some nonlinear evolution equations by utilizing the \((G'/G)\)-expansion method ⋮ The discrete (G′/G)-expansion method applied to the differential-difference Burgers equation and the relativistic Toda lattice system ⋮ New application of the \((\frac{G'}{G})\)-expansion method to higher-order nonlinear equations ⋮ Discrete exact solutions to some nonlinear differential-difference equations via the \((G'/G)\)-expansion method ⋮ A method for constructing nontraveling wave solutions for (1+1)-dimensional evolution equations

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