Solitary wave solution of nonlinear Bogoyavlenskii system by variational analysis method

In this work, the Bogoyavlenskii system (BS) and fractal BS are investigated by variational method for the first time. An efficient and simple scheme is proposed to seek their exact solitary wave solutions, which is called variational analysis method. The novel scheme requires only two steps, making it much attractive in practical applications, and a good result is obtained. This paper cleans up the road to the exact solitions, and it sheds a new light on the soliton theory. Finally, the physical properties of solitary wave solutions obtained are analyzed by some simulation figures.

Exact solutions of the (3+1)-dimensional generalized Boiti–Leon–Manna–Pempinelli equation

In this paper, we study exact solutions of the (3[Formula: see text]+[Formula: see text]1)-dimensional Boiti–Leon–Manna–Pempinelli equation. We employ the Hirota bilinear method to obtain the multi-solitary wave solutions, soliton resonant solutions, periodic solutions and interactional solutions and periodic resonant solutions. The corresponding asymptotic features and images are also clearly given.

Solitary Wave Solutions for Some Fractional Evolution Equations via New Kudryashov Approach

In this work, we construct solitary wave solutions of a nonlinear evolution equation in the physical phenomena of waves;namely the time-fractional fifth-order Sawada-Kotera equation and the (4+1)-dimensional space-time fractional Fokas equation by Kudryashov method with a new function. As a result, new types of exact analytical solutions are obtained. Here the fractional derivative is described in beta sense.

Stability analysis and abundant closed-form wave solutions of the Date–Jimbo–Kashiwara–Miwa and combined sinh–cosh-Gordon equations arising in fluid mechanics

In this manuscript, several types of exact solutions including trigonometric, hyperbolic, exponential, and rational function are successfully constructed with the implementation of two modified mathematical methods, namely called extended simple equation and modified F-expansion methods on the (2 + 1)-dimensional Date–Jimbo–Kashiwara–Miwa and the combined sinh–cosh-Gordon equations. Diverse form of solitary wave solutions is achieved from exact solutions by passing the special values to the parameters. Some solution are plotted in the form of 3D and 2D by assigning the specific values to parameters under the constrain condition to the solutions. These approaches yield the new solutions that we think other researchers have missed in the field of nonlinear sciences. Hence the searched wave’s results are loyal to the researchers and also have imperious applications in applied sciences.