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In this study, we have successfully found some travelling wave solutions of the variant Boussinesq system and fractional system of two-dimensional Burgers' equations of fractional order by using the -expansion method. These exact solutions contain hyperbolic, trigonometric and rational function solutions. The fractional complex transform is generally used to convert a partial fractional differential equation (FDEs) with modified Riemann-Liouville derivative into ordinary differential equation. We showed that the considered transform and method are very reliable, efficient and powerful in solving wide classes of other nonlinear fractional order equations and systems.

Lineer olmayan olusum denklemleri (NLEE) cok sayida alanda ortaya cikan problemlerin matematiksel modelleri icin temel olusturur. Gecmis yillarda, uygulamali matematikte olusum denklemleri onemli bir yer kazanmistir. Bu calisma, lineer olmayan olusum denklemleri (NLEE) icin perturbasyon yontemi olarak bilinen cok olcekli acilim metoduyla ilgilidir. Bu raporda, (1 + 1) boyutlu besinci mertebeden lineer olmayan Caudrey-Dodd-Gibbon (CDG) denkleminin analizi icin cok olcekli acilim metodu uygulanmistir ve lineer olmayan Schrodinger (NLS) tipi denklemi elde edilmistir.

WOS: 000394270500011, In this work, we have considered the modified simple equation (MSE) method for obtaining exact solutions of nonlinear fractional-order differential equations. The space-time fractional equal width (EW) and the modified equal width (mEW) equation are considered for illustrating the effectiveness of the algorithm. It has been observed that all exact solutions obtained in this paper verify the nonlinear ordinary differential equations which was obtained from nonlinear fractional-order differential equations under the terms of wave transformation relationship. The obtained results are shown graphically., Anadolu University Scientific Research Projects [1602E048], This work was partly supported by Anadolu University Scientific Research Projects (Grant No: 1602E048).

We perform a multiple scales analysis on the modified nonlinear Schrödinger (MNLS) equation in the Hamiltonian form. We derive, as amplitude equations, Korteweg-de Vries (KdV) flow equations in the bi-Hamiltonian form.

We perform a multiple-time scales analysis and compatibility condition to the short-wave model equation. We derive Korteweg–de Vries flow equation in the bi-Hamiltonian form as an amplitude equation. Copyright © 2013 John Wiley & Sons, Ltd.

11th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences (ICNPAA) -- JUL 04-08, 2016 -- Univ La Rochelle, La Rochelle, FRANCE, WOS: 000399203000082, Nonlinear evolution equation (NLEE) systems model the most essential topics in nonlinear sciences. Exact solutions of these equations play a major role in the suitable understanding of mechanisms of the various physical phenomena modelled by these NLEEs. For this reason, searching exact solutions of these equations have taken intense interest lately. In the present work, we have obtained new exact solutions of the and Kaup-Boussinesq systems with the generalized Kudryashov method., Amer Inst Aeronaut & Astronaut, Int Federat Nonlinear Analysts, Int Federat Informat Proc, Assoc Francaise Mecanique, Aquitaine Limousin PoitouCharente Reg, Charente Maritime Dept, Lab Sci Ingenieur Environnement, Anadolu University, Scientific Research Project (BAP) [1602E048], This research is supported by Anadolu University, Scientific Research Project (BAP), Project Number: 1602E048.

WOS: 000329559200009, We perform a multiple scale analysis on the fourth order nonlinear Schrodinger equation in the Hamiltonian form together with the Hamiltonian function. We derive, as amplitude equations, Korteweg-de Vries flow equations in the bi-Hamiltonian form with the corresponding Hamiltonian functions. Copyright (c) 2013 John Wiley & Sons, Ltd.

WOS: 000264296000004, In this paper, we established travelling wave Solutions for some (2 + 1)-dimensional nonlinear evolution equations. The first integral method was used to construct travelling wave solutions of nonlinear evolution equations. The travelling wave solutions are expressed by the hyperbolic functions, the trigonometric functions and the rational functions. The first integral method presents a wider applicability for handling nonlinear wave equations

In this report, a method of multiple scales is presented for the analysis of the (1+1)-dimensional seven order Korteweg-de Vries (KdV7) equation and we derive nonlinear Schrodinger (NLS) type equation. Also we found the exact solutions for (1+1)-dimensional KdV7 equation by using the ( G/G )-expansion method. These methods are very simple and effective for getting integrability and exact solutions of KdV type equations