Browsing by Author "Hosseini K."

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Exact traveling wave solutions of the Wu–Zhang system describing (1 + 1)-dimensional dispersive long wave
(2017-12-01) Kaplan M.; Mayeli P.; Hosseini K.
This paper examines the effectiveness of two newly developed algorithms called the exponential rational function and modified simple equation methods in exactly solving a well-known nonlinear system of partial differential equations. In this respect, the Wu–Zhang system which describes (1 + 1)-dimensional dispersive long wave is considered, and as an achievement, a series of exact traveling wave solutions for the aforementioned system are formally extracted.
Investigation of exact solutions for the Tzitzéica type equations in nonlinear optics
(2018-02-01) Kaplan M.; Hosseini K.
In this paper we consider the Tzitzéica type equations and establish the travelling wave transformation which turns the nonlinear evolution equations into the ordinary differential equations, then we obtain exact solutions of the Tzitzéica-Dodd-Bullough equation, the Tzitzéica equation and the Dodd-Bullough-Mikhailov equation by using the exponential rational function method.
New Exact Traveling Wave Solutions of the Unstable Nonlinear Schrö dinger Equations
(2017-12-01) Hosseini K.; Kumar D.; Kaplan M.; Bejarbaneh E.Y.
The present paper studies the unstable nonlinear Schrödinger equations, describing the time evolution of disturbances in marginally stable or unstable media. More precisely, the unstable nonlinear Schrödinger equation and its modified form are analytically solved using two efficient distinct techniques, known as the modified Kudraysov method and the sine-Gordon expansion approach. As a result, a wide range of new exact traveling wave solutions for the unstable nonlinear Schrödinger equation and its modified form are formally obtained.
On some novel solution solutions to the generalized Schrödinger-Boussinesq equations for the interaction between complex short wave and real long wave envelope
(2022-08-01) Kumar D.; Hosseini K.; Kaabar M.K.A.; Kaplan M.; Salahshour S.
This paper explores some novel solutions to the generalized Schrödinger-Boussinesq (gSBq) equations, which describe the interaction between complex short wave and real long wave envelope. In order to derive some novel complex hyperbolic and complex trigonometric function solutions, the sine-Gordon equation method (sGEM) is applied to the gSBq equations. Novel complex hyperbolic and trigonometric function solutions are expressed by the dark, bright, combo dark-bright, W-shaped, M-shaped, singular, combo singular, and periodic wave solutions. The accuracy of the explored solitons is examined under the back substitution to the corresponding equations via the symbolic computation software Maple. It is found from the back substitution outcomes that all soliton solutions satisfy the original equations. The proper significance of the explored outcomes is demonstrated by the three-dimensional (3D) and two-dimensional (2D) graphs, which are presented under the selection of particular values of the free parameters. All the combo-soliton (W-shaped, M-shaped, and periodic wave) solutions are found to be new for the interaction between complex short wave and real long wave envelope in laser physics that show the novelty of the study. Moreover, the applied method provides an efficient tool for exploring novel soliton solutions, and it overcomes the complexities of the solitary wave ansatz method.
Optical soliton solutions of the cubic-quintic non-linear Schrödinger’s equation including an anti-cubic term
(2018-07-12) Kaplan M.; Hosseini K.; Samadani F.; Raza N.
A wide range of problems in different fields of the applied sciences especially non-linear optics is described by non-linear Schrödinger’s equations (NLSEs). In the present paper, a specific type of NLSEs known as the cubic-quintic non-linear Schrödinger’s equation including an anti-cubic term has been studied. The generalized Kudryashov method along with symbolic computation package has been exerted to carry out this objective. As a consequence, a series of optical soliton solutions have formally been retrieved. It is corroborated that the generalized form of Kudryashov method is a direct, effectual, and reliable technique to deal with various types of non-linear Schrödinger’s equations.