Hybrid Dispersive Optical Solitons in Nonlinear Cubic-Quintic-Septic Schrödinger Equation

Abstract

Certain hybrid prototypes of dispersive optical solitons that we are looking for can correspond to new or future behaviors, observable or not, developed or will be developed by optical media that present the cubic-quintic-septic law coupled, with strong dispersions. The equation considered for this purpose is that of non-linear Schrödinger. The solutions are obtained using the Bogning-Djeumen Tchaho-Kofané method extended to the new implicit Bogning' functions. Some of the obtained solutions show that their existence is due only to the Kerr law nonlinearity presence. Graphical representations plotted have confirmed the hybrid and multi-form character of the obtained dispersive optical solitons. We believe that a good understanding of the hybrid dispersive optical solitons highlighted in the context of this work allows to grasp the physical description of systems whose dynamics are governed by nonlinear Schrödinger equation as studied in this work, allowing thereby a relevant improvement of complex problems encountered in particular in nonliear optaics and in optical fibers.

Hybridization of Solitary Wave Solutions in (2+1)-dimentional Complex Ginzburg-Landau Equation

“…In eq. ( 9), the respective coefficient terms A1 and A2 are hybrid solitary waves [22][23][24] while the respective coefficient terms B1 and B2 are the well known classic solitons under the names: Kink and Dark. Thereafter, the consideration of eq.…”

“…Faced with these complications, a good number of effective direct methods [14] to obtain the exact solutions of these models have been proposed, in particular the homoclinic test technique [15][16][17], Exp-function method [18], the F-expansion method [19], the extended tanhfunction method [20; 21], and so on. Hybrid solutions [22][23][24] formed by an assembly of analytical sequences of the classical solitary waves are very difficult to obtain. These last two decades have seen the birth of other techniques for solving some of the proposed models, which, apart from exact solutions, also offer approximate or forced solutions with several solitons, such as the Bogning-Djeumen Tchaho-Kofan é method (BDKm) [25][26][27][28][29][30] extended to the implicit Bogning functions(iB-functions) [29][30][31][32].…”

Dispersive analytical wave solutions of the strain waves equation in microstructured solids and Lax’ fifth-order dynamical systems

“…In the past some decades, novel exact solutions may help to find new phenomena. A variety of powerful techniques, such as inverse scattering scheme, [1,2] Hirota bilinear tranformation [3,4], the tanh-sech method [5][6][7][8], sine-cosine method [9,10], Expfunction method [11][12][13][14] and ¢ G G ( ) expansion methods [15][16][17][18][19][20], the Lie group symmetry method [21], the homotopy analysis scheme [22,23], the first integration technique [24],the theta function method [25,26], the homogeneous balance method [27], the Jacobi elliptic function method [28,29], the Adomian decomposition method [30] and Some new and important developments for searching for analytical solitary wave solutions for NLPDEs as [31][32][33][34][35][36][37][38][39][40][41] were used to develop nonlinear dispersive and dissipative nonlinear wave problems.…”