New complex exact travelling wave solutions for the generalized-Zakharov equation with complex structures

Abstract

Abstract. In this paper, we apply the sine-Gordon expansion method which is one of the powerful methods to the generalized-Zakharov equation with complex structure. This algorithm yields new complex hyperbolic function solutions to the generalized-Zakharov equation with complex structure. Wolfram Mathematica 9 has been used throughout the paper for plotting two-and three-dimensional surface of travelling wave solutions obtained.

Solving a well-posed fractional initial value problem by a complex approach

“…The ideas and methods of complex analysis have proven to be very important in certain analytical methods for differential equations: for example, the Fokas method [19][20][21] relies heavily on Cauchy's theorem for deforming complex contour integrals, and the d-bar method [1,22,23] is based on using the complex d-bar derivative related to the Cauchy-Riemann equations. Some of these complex definitions and methods have recently been extended into fractional calculus, in some papers on complex methods for fractional differential equations [9,12,17] and the very recent fractionalisation of the complex d-bar derivative [18], although historically the connections between complex analysis and fractional calculus have not been deeply explored. Therefore, all indications are that complex methods will be equally useful in fractional calculus as in classical calculus, but a lot of work still needs to be done in developing this area.…”

A New Approach to (3+1) Dimensional Boiti–Leon–Manna–Pempinelli Equation

“…Hence, there are various analytical methods in the literature used by researchers to obtain solutions for such equations. Some of these are the multipliers method [1],the simplest equation method [2], the (G /G)-expansion method [3][4][5][6], the Sine-Gordon expansion method [7][8][9][10][11],the extended trial equation method [12,13], the new function method [14,15]. In this study, we used the Modified Exponential Function Method (MEFM) to the (3+1) dimensional Boiti-Leon-Manna-Pempinelli equation (BLMP) which is used to describe incompressible liquid in fluid mechanics.…”

Optical Soliton Solutions of Fokas-Lenells Equation via (m + 1/G')- Expansion Method

“…The connection between nonlinear complex physical phenomena and nonlinear partial differential equations (NLPDEs) is involved in many fields of sciences such as plasma physics, optical fibers, nonlinear optics, fluid mechanics, biology, chemistry kinetics, geochemistry, engineer ing, and so on [2]. NLPDEs have different analytical approaches used to find analytical solutions [11][12][13][17][18][19]. Different analytical approaches used to find the soliton solutions of the Fokas-Lenells equation as well as thecoupled Fokas-Lenells equation like the −!…”