New solitary wave solutions of some nonlinear models and their applications

Abstract

In this manuscript, we utilize the algorithm of (G /G) expansion method to construct new solutions of three important models, the Ablowitz-Kaup-Newell-Segur water wave equation, the (2 + 1)-dimensional Boussinesq equation, and the (3 + 1)-dimensional Yu-Toda-Sasa-Fukuyama equation, having numerous application in plasma physics, fluid dynamics, and optical fibers. Some new types of traveling wave solutions are acquired, which have not been obtained previously by using this our new technique. The achieved solutions appear with all necessary constraint conditions, which are compulsory for them to exist. The constructed new solutions have vital applications in applied sciences. To understand the physical phenomena of these models, we have also presented graphically movements of the obtained results. It is shown that the our technique provides a more powerful mathematical tool for constructing exact traveling wave solutions for many other nonlinear waves models in mathematics and physics.

Geometric process solving a class of analytic functions using q-convolution differential operator

“…For extra investigation, we inform the investigators to give some results and consequences related to other categories of smooth functions for instant, one can use harmonic mappings, p-valent or meromorphic maps. Moreover, El-Qadeem and Mamon [11] can use (7) to generalize their classes by extend the operator into p-valent class of analytic functions or generalize works in [29][30][31][32][33][34][35][36].…”

Some New Traveling Wave Solutions of Nonlinear Fluid Models via the MSE Method

“…However, exact solutions of equations in the nonlinear form are not always obtained by classical methods. In recent times, many useful methods and techniques such as the modified simple equation (MSE) method [7], the improved tan(ϕ/2)-expansion method [8], the extended rational sine-cosine method [9], the (G /G, 1/G)-expansion method [10], the improved F-expansion method [11], the modified exp (−φ (ε))-expansion method [12], the first integral method [13], the (G /G)-expansion method [14] etc. have been enhanced to find traveling wave solutions.…”

Iterative Analysis of Nonlinear BBM Equations under Nonsingular Fractional Order Derivative

“…One of the important aspects is the existence theory of solution which has given proper attention in the last years [5][6][7][8][9][10][11]. By using the fixed point theory, the existence theory to numerous problems has been established [12][13][14][15][16]. The authors in [17][18][19][20][21][22] also studied different aspects of FODEs using a derivative with nonsingular kernel and Laplace transform.…”