On solving two higher-order nonlinear PDEs describing the propagation of optical pulses in optic fibers using the $$\left( \frac{G^{\prime }}{G},\frac{1}{G}\right) $$ G ′ G , 1 G -expansion method

Abstract

The propagation of the optical solitons is usually governed by the nonlinear Schrodinger equations. In this article, the two variable \((\frac{ G^{\prime }}{G},\frac{1}{G})\)-expansion method is employed to construct the exact traveling wave solutions with parameters of two nonlinear PDEs namely, the (2\(+\)1)-dimensional nonlinear cubic–quintic Ginzburg–Landau equation and the (1\(+\)1)-dimensional resonant nonlinear Schrodinger’s equation with dual-power law nonlinearity which describe the propagation of optical pulses in optic fibers. When the parameters are replaced by special values, the well-known solitary wave solutions of these equations rediscovered from the traveling waves. This method can be thought of as the generalization of well-known original \((\frac{G^{\prime }}{G})\)-expansion method proposed by M. Wang et al. It is shown that the two variable \((\frac{G^{\prime }}{G}, \frac{1}{G})\)-expansion method provides a more powerful mathematical tool for solving many other nonlinear PDEs in mathematical physics.