<abstract><p>This article describes the construction of optical solitons and single traveling wave solutions of Biswas-Arshed equation with the beta time derivative. By using the polynomial complete discriminant system method, a series of traveling wave solutions are constructed, including the rational function solutions, Jacobian elliptic function solutions, hyperbolic function solutions, trigonometric function solutions and inverse trigonometric function solutions. The conclusions of this paper comprise some new and different solutions that cannot be found in existing literature. Using the mathematic software Maple, the 3D and 2D graphs of the obtained traveling wave solutions were also developed. It is worth noting that these traveling wave solutions may motivate us to explore new phenomena which may be appear in optical fiber propagation theory.</p></abstract>

The principal objective of this article is to construct new exact soliton solutions of the (2 + 1)-dimensional Heisenberg ferromagnetic spin chain equation which investigates the nonlinear dynamics of magnets. Through using the complete discrimination system method, the traveling wave solutions are obtained. As a result, we get the traveling wave solutions of the Heisenberg ferromagnetic spin chain equation, which include rational function solutions, Jacobian elliptic function solutions, hyperbolic function solutions, trigonometric function solutions, inverse trigonometric function, logarithmic function. Some graphical representations of the problems and that of comparison are also provided.

In this paper, the complete discrimination system method is used to construct the single traveling wave solutions for the ( 3 + 1 )-dimensional Jimbo-Miwa equations with space-time fractional derivative. As a result, we get the exact traveling wave solutions of the ( 3 + 1 )-dimensional Jimbo-Miwa equation with space-time fractional derivative, which include rational function solutions, Jacobian elliptic function solutions, hyperbolic function solutions, and trigonometric function solutions. Some graphical representations of the solutions are also provided. Finally, the obtained solution is compared with the existing literature.

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