Mehmet Ekici

Extended trial equation method to generalized nonlinear partial differential equations

In this article, we give the extended trial equation method for solving nonlinear partial differential equations with higher order nonlinearity. By use of this method, the exact traveling wave solutions including soliton solution, singular soliton solutions, rational function solution and elliptic integral function solution to one-dimensional general improved KdV (GIKdV) equation and R(m,n) equation are obtained. Also, a more general trial equation method is proposed.

Nematicons in liquid crystals by extended trial equation method

This paper employs extended trial equation method to retrieve nematicons in liquid crystals from its governing equation. In addition, several other forms of solution naturally emerged from the integration algorithm. These are shock waves, singular solitons, snoidal waves, periodic singular waves, plane waves and others. These variety of solutions are being reported for the first time in the context of liquid crystals.

The investigation of soliton solutions of the coupled sine-Gordon equation in nonlinear optics

Abstract The coupled sine-Gordon equation, which can be used to describe the propagation of an optical pulse in fibre waveguide, has been investigated analytically. The hyperbolic and trigonometric function solutions are constructed by the extended expansion method, and then the Jacobi elliptic, hyperbolic and trigonometric function solutions are derived with the help of the extended Jacobi elliptic function expansion method.

Analytical study of solitons to Biswas-Milovic model in nonlinear optics

Optical solitions to the Biswas–Milovic model have been investigated analytically with the help of the generalized Kudryashov method. Four types of nonlinear are considered. They are Kerr law, Power law, parabolic law and dual-power law. As a result, exact solitary wave solutions are obtained.

Optical solitons of some fractional differential equations in nonlinear optics

Abstract This paper deals with two different forms of the conformable fractional Benjamin–Bona–Mahony (BBM) equations by an analytical method. These physical models have important applications for describing the propagation of optical pulses in non-linear media. The conformable fractional symmetric BBM equation and the conformable time fractional Equal-width (EW) equation are considered. The extended Jacobi’s elliptic function expansion scheme are used to extract explicit solitons.

F-expansion method and new exact solutions of the Schrödinger-KdV equation.

F-expansion method is proposed to seek exact solutions of nonlinear evolution equations. With the aid of symbolic computation, we choose the Schrödinger-KdV equation with a source to illustrate the validity and advantages of the proposed method. A number of Jacobi-elliptic function solutions are obtained including the Weierstrass-elliptic function solutions. When the modulus m of Jacobi-elliptic function approaches to 1 and 0, soliton-like solutions and trigonometric-function solutions are also obtained, respectively. The proposed method is a straightforward, short, promising, and powerful method for the nonlinear evolution equations in mathematical physics.

Solitons and other solutions to Wu–Zhang system

Mohammad Mirzazadeh, Mehmet Ekici, Mostafa Eslami, Edamana Vasudevan Krishnan, Sachin Kumar, Anjan Biswas Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran mirzazadehs2@gmail.com Faculty of Science and Arts, Bozok University, 66100 Yozgat, Turkey ekici-m@hotmail.com Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran meslami.edu@gmail.com Department of Mathematics and Statistics, Sultan Qaboos University, P.O. Box 36, Al-Khod 123, Muscat, Oman krish@squ.edu.om Centre for Mathematics and Statistics, School of Basic and Applied Sciences, Central University of Punjab, Bathinda 151001, Punjab, India sachin1jan@yahoo.com Department of Mathematical Sciences, Delaware State University, Dover, DE 19901-2277, USA biswas.anjan@gmail.com Faculty of Science, King Abdulaziz University, Jeddah-21589, Saudi Arabia

Solitons in Nonlinear Directional Couplers with Optical Metamaterials by Trial Function Scheme

Solitons in Nonlinear Directional Couplers with Optical Metamaterials by Trial Function Scheme A.H. Arnous, M. Ekici, S.P. Moshokoa, M. Zaka Ullah, A. Biswasc,d∗and M. Belic Department of Physics and Engineering Mathematics, Higher Institute of Engineering, El-Shorouk, Cairo, Egypt Department of Mathematics, Faculty of Science and Arts, Bozok University, 66100 Yozgat, Turkey Department of Mathematics and Statistics, Tshwane University of Technology, Pretoria-0008, South Africa Operator Theory and Applications Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box-80203, Jeddah-21589, Saudi Arabia Science Program, Texas A&M University at Qatar, P.O. Box 23874, Doha, Qatar

Soliton Solutions of the Klein-Gordon-Zakharov Equation with Power Law Nonlinearity

We introduce a new version of the trial equation method for solving nonintegrable partial differential equations in mathematical physics. Some exact solutions including soliton solutions and rational and elliptic function solutions to the Klein-Gordon-Zakharov equation with power law nonlinearity in (1