Mehmet Naci Özer

Solving nonlinear evolution equation system using two different methods

Abstract This paper deals with constructing more general exact solutions of the coupled Higgs equation by using the (G0/G, 1/G)-expansion and (1/G0)-expansion methods. The obtained solutions are expressed by three types of functions: hyperbolic, trigonometric and rational functions with free parameters. It has been shown that the suggested methods are productive and will be used to solve nonlinear partial differential equations in applied mathematics and engineering. Throughout the paper, all the calculations are made with the aid of the Maple software.

Complexiton solutions for two nonlinear partial differential equations via modification of simplified Hirota method

In this study, we obtain complexiton solutions of Sawada–Kotera equation and ninth-order KdV equation. For this cause, we employ Wazwaz and Zhaqilao’s method which can be regarded as generalization of simplified Hirota method through extension real parameters into complex parameters. Special conditions to distinguish complexiton, soliton, and soliton–complexiton interaction solutions from each other are given.

Derivation of Korteweg–de Vries flow equations from the regularized long-wave (RLW) equation

Abstract We perform a multiple-time scales analysis and compatibility condition to the regularized long-wave (RLW) equation. We derive Korteweg–de Vries (KdV) flow equation in the bi-Hamiltonian form as an amplitude equation.