On the Complex Mixed Dark-Bright Wave Distributions to Some Conformable Nonlinear Integrable Models

Abstract

In this research paper, we implement the sine-Gordon expansion method to two governing models which are the (2+1)-dimensional Nizhnik–Novikov–Veselov equation and the Caudrey–Dodd–Gibbon–Sawada–Kotera equation. We use conformable derivative to transform these nonlinear partial differential models to ordinary differential equations. We find some wave solutions having trigonometric function, hyperbolic function. Under the strain conditions of these solutions obtained in this paper, various simulations are plotted.

Fractional Order Environmental and Economic Model Investigations Using Artificial Neural Network

“…In future studies, the ANNs-LMBM approaches have been used to solve the numerical performance of the nonlinear models [35][36][37][38][39][40][41][42].…”

Computational and numerical wave solutions of the Caudrey–Dodd–Gibbon equation

“…(2) is an integrable model with multiple-solution answers [30] . This equation is used to solve complicated issues in solid–state physics, nonlinear optics, plasma physics, fluid dynamics, mathematical biology, nonlinear optics, dislocations in crystals, kink dynamics, chemical kinetics, as well as quantum field theory [31] . Many computational strategies have been successfully employed in the development of various unique soliton wave solutions that provide a more hidden characterization of the shallow water wave [32] , [33] , [34] , [35] , [36] .…”

Analytical wave solutions of an electronically and biologically important model via two efficient schemes

“…Many different methods have been developed to gain analytical wave solutions of these NLPDEs, i.e., optical soliton solutions of coupled nonlinear Schrödinger equations have been gained with use of Kudryashov R-function technique, [1] some new kinds of optical soliton solutions of time-fractional perturbed nonlinear Schrödinger equations have been achieved by using the generalized Kudryashov scheme, [2] by applying the modified auxiliary equation technique, optical wave solutions of timefractional resonant nonlinear Schrödinger equations have been obtained, [3] new optical wave solutions for the time-fractional perturbed nonlinear Schrödinger equations have been achieved by utilizing the improved tan[φ (ζ /2)]-expansion scheme, [4] different kinds of optical wave solitons of time-fractional paraxial wave equations have been gained by using the Sardar sub-equation method, [5] various optical wave solutions of three-component coupled nonlinear Schrödinger equations have been attained with the help of generalized exponential rational function scheme, [6] dark, bright, singular and periodic solitary wave solutions of generalized fractional Davey-Stewartson equations have been obtained by applying the generalized projective Riccati equation technique, [7] some exact wave solutions of the Lax equation have been achieved by applying the extended sinh-Gordon expansion technique, [8] kink solitons of the Sharma-Tasso-Olver-Burgers equation have been attained by using Kudryashov and exponential techniques, [9] traveling wave solutions of perturbed Biswas-Milovic equations have been gained with the use of improved F-expansion technique, [10] some new optical wave solutions of complex Korteweg-de Vries equations have been obtained by applying the unified scheme. [11] Similarly, Hirota bilinear method, [12] modified extended tanh expansion method, [13] modified simplest equation technique, [14] extended Jacobi elliptic function scheme, [15] sech and tanh function solutions are obtained by using the sine-Gordon expansion scheme, [16] sinh, cosh, sin and cos involving solutions are gained by utilizing the rational sine-Gordon expansion technique [17] and many other techniques. [18][19][20][21][22][23][24] In this study, we use two schemes, i.e., the exp a function and extended sinh-Gordon equation expansion (EShGEE) schemes.…”