Exact traveling wave solutions for (2+1)-dimensional Konopelchenko-Dubrovsky equation by using the hyperbolic trigonometric functions methods

Abstract

In this research, the extended rational sinh-cosh method and the modified extended tanh-function method for mathematically constructing traveling wave solutions to the (2+1)-dimensional integro-differential Konopelchenko-Dubrovsky evolution equation are successfully employed to obtain specific appropriate solutions for the first time. A traveling wave transformation was utilized to turn the provided model into a third-order nonlinear ordinary differential equation. Solitary and periodic wave solutions for the model under investigation are obtained in terms of various complex hyperbolic trigonometric and rational functions. Several of the aforementioned solutions have been represented by two- and three-dimensional graphics with appropriate arbitrary parameters to highlight their physical implications. Two-dimensional graphs have presented the influence of time evolution on the solution’s structures.

Exact Solutions of the Stochastic Conformable Broer–Kaup Equations

“…In this section, the modified exponential function method will be used to obtain the traveling wave solutions that provide stochastic conformable Broer-Kaup equations. If wave transform (10) is applied to Equations ( 1) and (2), given above as stochastic conformable Broer-Kaup equations, the following nonlinear ordinary differential equations are found:…”

“…There are various effective methods or techniques in the literature for obtaining solutions and examining the behavior of these models. Some of these were seen as a result of the literature review as follows: the homotopy perturbation method and homotopy analysis method [1]; Adomian decomposition method [2]; the shifted Chebyshev tau method [3]; semi-analytical method [4]; analytical method [5,6]; generalized Kudryashov method [7]; sine-Gordon expansion method [8]; Jacobi elliptic function expansion method [9]; the hyperbolic trigonometric functions methods [10]; exp-function method [11]; modified extended tanh-function method [12]; new function method [13]; and modified exponential function method [14][15][16].…”

New soliton solutions of kraenkel-manna-merle system with beta time derivative

“…Nonlinear evolution equations (NLEEs) have important applications in mathematical chemistry, mathematical physics, hydrodynamics, biophysics, geochemistry, control theory, mechanics, meteorology, chemical kinematics, optics, biogenetics and many other fields of science. Many researchers have presented various solution methods to obtain the solutions of NLEEs [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20].…”

Classification of single-wave and bi-wave motion through fourth-order equations generated from the Ito model

“…In this paper, we aim to study the wave propagation in Wazwaz's equations using three techniques: Modified rational sine-cosine functions [5][6][7][8], Kudryashov-expansion [9][10][11][12], and Hirota bilinear forms [13][14][15][16][17][18]. Our focus will mainly be on the second fourth-order Wazwaz equation, which is a generalized form of the first Wazwaz equation.…”