Reham M. A. Shohib

The fractional complex transformation for nonlinear fractional partial differential equations in the mathematical physics

Abstract In this article, the modified extended tanh-function method is employed to solve fractional partial differential equations in the sense of the modified Riemann–Liouville derivative. Based on a nonlinear fractional complex transformation, certain fractional partial differential equations can be turned into nonlinear ordinary differential equations of integer orders. For illustrating the validity of this method, we apply it to four nonlinear equations namely, the space–time fractional generalized nonlinear Hirota–Satsuma coupled KdV equations, the space–time fractional nonlinear Whitham–Broer–Kaup equations, the space–time fractional nonlinear coupled Burgers equations and the space–time fractional nonlinear coupled mKdV equations.

Solitons and other solutions for higher-order NLS equation and quantum ZK equation using the extended simplest equation method

Abstract In this article, we apply the extended simplest equation method for constructing the solitons and other solutions of two nonlinear partial differential equations (PDEs), namely the higher-order nonlinear Schrodinger (NLS) equation with derivative non-Kerr nonlinear terms and the nonlinear quantum Zakharov–Kuznetsov (QZK) equation which play an important role in mathematical physics. The first equation describes pulse of the propagation beyond ultrashort range in optical communication systems, while the second equation arises in quantum magneto plasma. Comparison of our new results in this article with the well-known results is given.

Comment on " Application of Improved - Expansion Method to Traveling Wave Solutions of Two Nonlinear Evolution Equations, Adv. Appl. Math. Mech. 4(2012) 122-130"

The authors of the above article proposed the improved ( / ) G G  expansion method and found some traveling wave solutions for each of two nonlinear evolution equations in mathematical physics, namely the Regularized Long Wave (RLW) equation and the Symmetric Regularized Long Wave (SRLW) equation. In the present article, we have noted that if we use a suitable transformation, the improved (G’/G)expansion method can be reduced into the well -known generalized Riccati equation mapping method which provides us with much more traveling wave solutions, namely twenty seven solutions for each of these two nonlinear evaluation equations. Comparison between the results of these two methods is presented. General Terms 02.30.Jr, 05.45.Yv, 02.30.Ik