Optical Solitons With M-Truncated and Beta Derivatives in Nonlinear Optics

Abstract

This paper studies optical solitons with M-truncated and beta derivatives (BD) for the Complex Ginzburg-Landau equation (CGLE) with Kerr Law nonlinearity. Two well-known integration schemes which are generalized tanh method (GTM) and generalized Bernoulli sub-ODE method (GBM) are utilized to extract such optical soliton solutions. For the successful existence of the solutions, the constraints conditions have been presented. The discussion for the physical features of the obtained solutions is reported.

Rogue Wave Solutions and Modulation Instability With Variable Coefficient and Harmonic Potential

“…Six small peaks appear around the one high peak of the second-order solution. Graphical representations of second-order rogue waves with both GF and EMF are also shown in Figures 2D-F. Graphical representations of the amplitudes given by equation (30) at a 0 = 1 and γ (t) = t are depicted in Figures 3A-D with the different parameter values. The curves in Figures 3A,B are formed under the GF, and those in Figures 3C,D are formed when both the GF and EMF are present.…”

“…These waves are also found in deep and shallow water and, beyond oceanic expanses, in optical fibers [1][2][3][4][5][6][7][8], super fluids, and so on [9][10][11][12][13][14][15][16][17][18]. In recent times, the theoretical study of these kinds of waves has become an interesting part of the field of nonlinear sciences [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34]. The following section deals with the extraction of wave solutions with ST.…”

New approximate analytical solutions for the nonlinear fractional Schrödinger equation with second‐order spatio‐temporal dispersion via double Laplace transform method

“…The PDEs, particularly the Schrödinger equation, have been applied in several applications in physics and engineering due to the importance of this equation in nonlinear optics, which can successfully explain the dynamics of optical soliton propagation in optical fibers. Optical solutions for the complex Ginzburg-Landau equation with Kerr law nonlinearity formulated in the senses of truncated M-fractional derivative and beta derivative were investigated in Khalil et al 25 In addition, optical solitons for Kundu-Eckhaus equation were obtained via the methods of modified tanh coth and extended Jacobi elliptic function expansion 26 and the first integral method, 27 respectively. Optical solitons were also studied for various other models in nonlinear optics (see several works [28][29][30][31][32][33] ).…”

New Solitary Wave Solutions for Variants of (3+1)-Dimensional Wazwaz-Benjamin-Bona-Mahony Equations

“…Exact solutions produce corporal information to describe the physical behavior of system connected with these NLEs. In recent years, several efficient methods including method of extended tanh [1,2], tanh-coth [3,4], Hirota's direct [5,6], sine-cosine [7,8], extended direct algebraic [9,10], extended trial approach [11,12], Exp [-ϕ(ξ)]-Expansion [13,14], a new auxiliary equation [15,16], Jacobi elliptic ansatz [17,18], generalized Bernoulli sub-ODE [19,20], functional variable [21,22], sub equation [23,24], and so on [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39], have been established for efficient solutions of NLEs.…”