Folded novel accurate analytical and semi-analytical solutions of a generalized Calogero–Bogoyavlenskii–Schiff equation

Abstract

This paper studies the analytical and semi-analytic solutions of the generalized Calogero–Bogoyavlenskii–Schiff (CBS) equation. This model describes the (2 + 1)–dimensional interaction between Riemann-wave propagation along the y-axis and the x-axis wave. The extended simplest equation (ESE) method is applied to the model, and a variety of novel solitary-wave solutions is given. These solitary-wave solutions prove the dynamic behavior of soliton waves in plasma. The accuracy of the obtained solution is verified using a variational iteration (VI) semi-analytical scheme. The analysis and the match between the constructed analytical solution and the semi-analytical solution are sketched using various diagrams to show the accuracy of the solution we obtained. The adopted scheme’s performance shows the effectiveness of the method and its ability to be applied to various nonlinear evolution equations.

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

“…Studying the investigated model through the He's variational iteration technique [41] , [42] , [43] along with Eq. (6) , gets the following numerical solution Using the constructed solution (Eq.…”

Optimal Control Problems for Hilfer Fractional Neutral Stochastic Evolution Hemivariational Inequalities

“…Due to their applications in viscoelasticity materials, electrical circuits, neural networks, control theory, chemistry, engineering, biology, mechanics, and physics, fractional differential equations (FDEs) have become a popular research topic ( [8][9][10][11][12][13][14]). We point out that during the past three decades, FDEs have undergone a substantial evolution (see, for instance, [15][16][17][18][19][20]) and are a useful instrument for the description of specific materials and processes [21][22][23][24][25][26][27][28][29][30].…”

Novel and accurate solitary wave solutions of the conformable fractional nonlinear Schrödinger equation

“…18 As a result, numerous computational, semi-analytical, and numerical techniques have been developed, including the extended simplest equation method, the extended tanh expansion method, the generalized Kudryashov method, the modified Khater method, the Sin-Cos expansion method, the Sech-Tanh expansion method, the Sine-Gordon expansion method, and the new auxiliary equation method. [19][20][21][22][23] However, there is no one-sizefits-all analytical technique for all nonlinear evolution problems. [24][25][26] In this context, we used the Khater II scheme to the 3-FNLS [27][28][29][30][31] to evaluate an unlimited number of solutions and then used the TQBS scheme 32,33 to determine the absolute value of error between the precise and numerical solutions.…”