In this study, extended trial equation method (ETEM) is implemented to obtain exact solutions of the Dullin-Gottwald-Holm Dynamical (DGHDE) and strain wave equation. We constitute some such as soliton solutions, rational, Jacobi elliptic, periodic hyperbolic function these equations via ETEM. Then, we present results that obtained by using method.

In this work, the F-expansion method is used to find exact solutions of space-time fractional modified Benjamin Bona Mahony equation and nonlinear time Schrödinger with beta derivative. One most efficient significant methods for obtaining new equations method. With aid Maple, more defined by Jacobi elliptic function are obtained. Hyperbolic some expressed trigonometric functions gained in case ...

The main goal of this paper is to give a modular type representation for the infinite product (1−x)(1−xq)(1−xq)(1−xq) · · · . It is shown that this representation essentially contains the well-known modular formulae either for Dedekind’s eta function, Jacobi theta function or for certain Lambert series. Thus a new and unified approach is outlined for the study of elliptic and modular functions ...

In this paper, we consider the (4+1)-dimensional fractional Fokas equation (FFE) with an M-truncated derivative. The extended tanh–coth method and Jacobi elliptic function are utilized to attain new hyperbolic, trigonometric, elliptic, rational solutions. addition, generalize some previous results. acquired solutions beneficial in analyzing definite intriguing physical phenomena because FFE is ...

In this paper, we apply the Miura transformation to construct the connection between a variablecoefficient KdV (vcKdV) equation and a variable-coefficient modified KdV (vcmKdV) equation under certain constraint. Solving the vcmKdV equation by use of the auxiliary equation method and using the Miura transformation, we find a rich variety of new exact solutions for the vcKdV equation, which inclu...

The fractional-stochastic Radhakrishnan-Kundu-Lakshmanan equation (FSRKLE) is considered here. To attain new hyperbolic, elliptic, rational, and trigonometric stochastic-fractional solutions, we use two various methods such as the sine-cosine Jacobi elliptic function methods. solutions acquired are important in understanding some interesting physical phenomena due to significance of designing p...