We apply a method based on the identification of coefficients of hyperbolic functions for the construction of the soliton solutions of the cubic and quintic nonlinear Ginzburg–Landau equations. This effective method improves the solution when the nonlinearity increases.

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In this work, we use the Bogning-Djeumen Tchaho-Kofané method to look for all solutions of shape Sech n -of the modified KdV and Born-Infeld Equations. n being a real number, we obtain the soliton solutions when n is positive and the non soliton solutions when n is negative.

The purpose of this paper is to extend the application of the modified, generalized, rational harmonic balance method to the determination of approximate analytical solutions to general single-degree-of-freedom oscillator equations. We propose a simple form of rational periodic function that depends on a parameter r such that 0<|r|<1 for the approximating solution. We show how one can determine this parameter analytically as a function of oscillation amplitude for a general nonlinear equation. Three examples are used to demonstrate the procedure and its accuracy.

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