Abstract
We construct the traveling wave solutions of some NonLinear Evolution Equations (NLEEs) with mutable coefficients arising in different branches of physics and mathematics. we apply a novel (G′G)-formalism to construct more general solitary traveling wave solutions of NLEEs such as Sharma-Tasso-Olver with mutable coefficients and Zakharov Kuznetsov equation. Interesting solutions of NLEEs are investigated by traveling wave solutions which are in form of trigonometric, rational, and hyperbolic functions. This may build more unified new solutions for different kinds of such NLEEs with mutable coefficients arising in mathematics and physics. Wolfram Mathematica 11 is used to perform the computation work and their corresponding plots and counter graphs are plotted. This method is found to be more useful and efficient for searching the exact solutions of NLEEs.
Highlights
NonLinear Evolution Equations (NLEEs) plays a significant role in the analysis of mathematical modeling and soliton theory. These NLEEs, which are primarily studied in mathematics and physics play an important role and character in various branches of science and technology, such as propagation of shallow water waves, population statistics physics, fluid dynamics, condensed matter physics, computational physics, and geophysics
It is more difficult to solve the NLEEs but, various methods have been tried for solving NLEEs, such as the Hirota’s bilinear operations [1] truncated Painleve expansion [2], inverse scattering transform [3], extended tanh-function method [4], F-expansion method [5], tanh-coth method [6], Jacobi-elliptic function expansion [7], homogenous balance method [8], sub ODE method
[9], Rank analysis method [10], Extended and modified direct algebraic method [11], extended mapping method [12, 13] and Seadawy techniques to find solutions for some nonlinear partial differential equations [14] and many other ansatzes comprising exponential and hyperbolic functions are accurately used for the analytic analysis of NLEEs
Summary
NonLinear Evolution Equations (NLEEs) plays a significant role in the analysis of mathematical modeling and soliton theory. These NLEEs, which are primarily studied in mathematics and physics play an important role and character in various branches of science and technology, such as propagation of shallow water waves, population statistics physics, fluid dynamics, condensed matter physics, computational physics, and geophysics. Tasso-Olver with mutable coefficients (STO) [21, 22] equation exact solutions are attained which are in form of hyperbolic, trigonometric and rational functions. Kuznetsov (ZK) equation [23] and abundant exact solutions are derived which included the trigonometric, rational, and hyperbolic functions. At the end of this article, discussion and conclusion are given in detail in the last section
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