Filiz Taşcan

Analytic solutions of the (2+1)-dimensional nonlinear evolution equations using the sine-cosine method

In this paper, we establish exact solutions for (2+1)-dimensional nonlinear evolution equations. The sine-cosine method is used to construct exact periodic and soliton solutions of (2+1)-dimensional nonlinear evolution equations. Many new families of exact traveling wave solutions of the (2+1)-dimensional Boussinesq, breaking soliton and BKP equations are successfully obtained. These solutions may be important of significance for the explanation of some practical physical problems. It is shown that the sine-cosine method provides a powerful mathematical tool for solving a great many nonlinear partial differential equations in mathematical physics.

Travelling wave solutions of the Cahn–Allen equation by using first integral method

Abstract In this paper, we established travelling wave solutions of the nonlinear equation. The first integral method was used to construct travelling wave solutions of the Cahn–Allen equation. The obtained results include periodic and solitary wave solutions. The power of this manageable method is confirmed.

The first-integral method applied to the Eckhaus equation

Abstract The first-integral method is a direct algebraic method for obtaining exact solutions of some nonlinear partial differential equations. This method can be applied to nonintegrable equations as well as to integrable ones. This method is based on the theory of commutative algebra. In this work, we apply the first-integral method to study the exact solutions of the Eckhaus equation.

Conservation Laws and Exact Solutions with Symmetry Reduction of Nonlinear Reaction Diffusion Equations

Abstract In this work we study one of the most important applications of symmetries to physical problems, namely the construction of conservation laws. Conservation laws have important place for applications of differential equations and solutions, also in all physics applications. And so, this study deals conservation laws of first- and second-type nonlinear (NL) reaction diffusion equations. We used Ibragimov’s approach for finding conservation laws for these equations. And then, we found exact solutions of first- and second-type NL reaction diffusion equations with Lie-point symmetries.

Applications of the first integral method to nonlinear evolution equations

In this paper, we establish travelling wave solutions for some nonlinear evolution equations. The first integral method is used to construct the travelling wave solutions of the modified Benjamin–Bona–Mahony and the coupled Klein–Gordon equations. The obtained results include periodic and solitary wave solutions. The first integral method presents a wider applicability to handling nonlinear wave equations.

Exact solutions of the Zoomeron and Klein–Gordon–Zakharov equations

Abstract The first integral method was used to construct exact solutions of the Zoomeron and Klein–Gordon–Zakharov equations. The obtained results include new soliton and periodic solutions. The work confirms the significant features of the employed method and shows the variety of the obtained solutions. Throughout the paper, all the calculations are made with the aid of the Maple packet program.

Conservation laws and Exact Solutions of Phi-Four (Phi-4) Equation via the (G′/G, 1/G)-Expansion Method

Abstract In this article, we constructed formal Lagrangian of Phi-4 equation, and then via this formal Lagrangian, we found adjoint equation. We investigated if the Lie point symmetries of the equation satisfy invariance condition or not. Then we used conservation theorem to find conservation laws of Phi-4 equation. Finally, the exact solutions of the equation were obtained through the (G′/G, 1/G)-expansion method.

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.

Quasi-periodic solutions of (3+1) generalized BKP equation by using Riemann theta functions

This paper is focused on quasi-periodic wave solutions of (3+1) generalized BKP equation. Because of some difficulties in calculations of N = 3 periodic solutions, hardly ever has there been a study on these solutions by using Riemann theta function. In this study, we obtain one and two periodic wave solutions as well as three periodic wave solutions for (3+1) generalized BKP equation. Moreover we analyze the asymptotic behavior of the periodic wave solutions tend to the known soliton solutions under a small amplitude limit.

Soliton Solutions, Bäcklund Transformation and Lax Pair for Coupled Burgers System via Bell Polynomials

Abstract In this work, we apply the binary Bell polynomial approach to coupled Burgers system. In other words, we investigate possible integrability of referred system. Bilinear form and soliton solutions are obtained, some figures related to these solutions are given. We also get Bäcklund transformations in both binary Bell polynomial form and bilinear form. Based on the Bäcklund transformation, Lax pair is obtained. Namely, this is a study in which integrabilitiy of coupled burgers system is investigated.