Application of Multiple Exp-Function Method to Obtain Multi-Soliton Solutions of (2 + 1)- and (3 + 1)-Dimensional Breaking Soliton Equations

Abstract

The multiple exp-function method is a new approach to obtain multiple wave solutions of nonlinear partial differential equations (NLPDEs). By this method one can obtain multi-soliton solutions of NLPDEs. In this paper, using computer algebra systems, we apply the multiple exp-function method to construct the exact multiple wave solutions of the (2 + 1)-and the (3 + 1)-dimensional breaking soliton equations. By this application, we obtain one-wave, two-wave and three-wave solutions for these equations.

Abundant Bounded and Unbounded Solitary, Periodic, Rogue‐Type Wave Solutions and Analysis of Parametric Effect on the Solutions to Nonlinear Klein–Gordon Model

“…For β < 0 and a 2 1 c 2 > 36βα 2 k 2 or β < 0 and a 2 1 c 2 < 36βα 2 k 2 , the solution ( 7) is a real-valued function solution, and it can be expressed as the hyperbolic function in equations ( 10)- (12). ese solutions always provide different types of solitary waves.…”

“…Many scientific experimental models are employed in nonlinear differential form from the phenomena of nonlinear fiber optics, high-amplitude waves, fluids, plasma, solid state particle motions, etc. Surveying literature, we realized ideas that many scientists worked to disclose innovative, efficient techniques for explaining internal behaviors of NLDEs with constant coefficients that are significant to elucidate different intricate problems such as a discrete algebraic framework [1], IRM-CG method [2], transformed rational function scheme [3], fractional residual method [4], new multistage technique [5], new analytical technique [6], extended tanh approach [7], Hirota-bilinear approach [8][9][10], multi exp-expansion method [11,12], Jacobi elliptic expansion method [13,14], Lie approach [15], Lie symmetry analysis techniques [16], generalized Kudryashov scheme [17,18], generalized exponential rational function scheme [19], MSE method [20][21][22], and many more. Such or similar schemes are also used to solve the model with variable coefficients to visualize various new nonlinear dynamics [23][24][25].…”

On some novel solitons solutions to the generalized (3 + 1)-dimensional Boiti-Leon-Manna-Pempinelli model using two different approaches

“…Xu developed four types of lump solutions using the Painleve-Backlund transformation [36,37], with two N exponential functions and quadratic functions. The multiple exponential function approaches [38,39] and scale transformation approaches [40,41] were also used to investigate the BLMP equation by Tang and Zai. Ma et al, being used to calculate the precise three-wave solutions.…”

Two New Modifications of the Exp-Function Method for Solving the Fractional-Order Hirota-Satsuma Coupled KdV

“…Recently, the fractional differential equations have become the focus of many scientists in the field of physics and mathematics and also many researchers to focus on this topic [3][4][5][6]. It can provide many methods for obtaining their exact solutions, such as the G ′ /G-expansion method [7][8][9], the exp-function method [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28], the homotopy analysis method [29,30], and spectral methods [31][32][33]. And in the meantime, obtaining the exact soliton solutions to these equations is more important because this study gives us a great deal of information on various sciences such as fluid mechanics, physics, and mathematics.…”