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This research focuses on the nonlinear coupled Davey–Stewartson Fokas system, which models pulse propagation in monomode optical fibers. In order to find the novel periodic and solitary wave solutions of the nonlinear coupled Davey–Stewartson Fokas system, we have employed two effective mathematical techniques named as the Sine‐Gordon expansion method and the simple equation method. We found after researching into previous literature that these novel solutions are unique and have never been reported. Some 3D and 2D graphs are also used to discuss the dynamical behavior of these new solutions. [ABSTRACT FROM AUTHOR]

In this work, the (2 + 1) -dimensional Kadomtsev–Petviashvili model is investigated. A novel variational scheme, namely, the variational transform wave method (VTWM), is successfully established to seek the solitary wave solution of the Kadomtsev–Petviashvili model. Furthermore, the fractal solitary solution of fractal Kadomtsev–Petviashvili model is also studied based on the local fractional derivative. Numerical examples are given to fully demonstrate that the VTWM is straightforward, efficient and attractive. Finally, the physical properties of solitary wave solutions are demonstrated by some 3D graphs. [ABSTRACT FROM AUTHOR]

In this paper, the fractional Schrödinger equation is described with beta derivative, which is used to elucidate the dynamic interaction of ultra-short pulses with quantum properties in optical fibers. This work is to study the solitary wave and periodic solutions of the fractional Schrödinger equation by employing three powerful and simple mathematical approaches like fractional Kudryashov method, fractional cosine–sine method and fractional tanh function method. The acquired outcomes illustrate that the proposed three computational approaches are simple, efficient, concise and can be adopted to study more complex phenomena. Finally, the dynamical behavior of these acquired solitary wave solutions is illustrated by sketching some 3D figures with proper parameters. [ABSTRACT FROM AUTHOR]

The primary objective of this study is to examine the behavior of the nonlinear Kaup-Newell equation. By employing the modified Kudryashov method and extended tanh function method, we have successfully derived novel solitary wave and periodic solutions. These new solutions are presented in trigonometric, hyperbolic and exponential function types. The proposed two approaches are efficient, direct and fascinating. These newly discovered solutions are illustrated using two-dimensional and three-dimensional graphs, incorporating suitable parameters values. These graphs are crucial for elucidating the dynamic properties of optical fibers. [ABSTRACT FROM AUTHOR]

The Klein–Gordon–Zakharov equation is an important and interesting model in physics. A fractional Klein–Gordon–Zakharov model is described by employing beta-derivative. Some new solitary wave solutions are acquired by utilizing the fractional rational sinh σ – cosh σ method and fractional sech σ method. Some 3D graphs are depicted to elaborate these new solitary wave solutions. The work is very helpful to study other related types of fractional evolution equations. [ABSTRACT FROM AUTHOR]

The coupled Boussinesq equation (CBE) acts a key role in modeling the shallow water waves of two-layer fluid flow. However, it becomes powerless for the nonsmooth boundary. So, a fractal modification of the CBE is suggested in this paper. Aided by the semi-inverse method, we successfully construct its fractal generalized variational principle. In addition, three recent techniques, namely, the Sardar-subequation method, He's frequency formulation method and subequation method, combined with the two-scale fractal dimension transform, are utilized to find abundant wave solutions. By these methods, various solutions expressed by the generalized hyperbolic functions, generalized trigonometric functions, hyperbolic functions and cosine function are obtained. With the aid of the mathematical software, the three-dimensional contours and two-dimensional curves are plotted to present the dynamic behaviors of the solutions. The results in this paper demonstrate that the proposed methods are powerful and effective to construct the traveling wave solutions of the fractal nonlinear evolution equations. [ABSTRACT FROM AUTHOR]