Optical solitons with anti-cubic nonlinearity using three integration schemes

Abstract

This paper employed three integration schemes to obtain soliton solutions in optical fibers with anticubic nonlinearity. These are traveling waves, tanh-coth scheme and finally the modified simple equation method. These yielded bright solitons, singular solitons, dark-singular combo solitons and other waves. The existence criteria for these solitons are presented. The paper concludes with a discussion on conservation laws.

Coupled soliton solutions of modeled equations in a Noguchi electrical line with crosslink capacitor

“…Considering the values of the following parameters A 10 V, 0 = B 10 V, 0 =h 10 m, 4 = -C 37 10 F, 1 10 =´-C C 37 10 F 370 10 F, Considering the values of the following parameters A 10 V, 0 = B 10 V, 0 =h 10 m, 4 = -C 37 10 F, 1 10 =´-C C 37 10 F 370 10 F,…”

“…We have in this regard decided to come up with definitions of nonlinear charges of capacitors constituting the two nonlinear parts linked through the capacitors in the said line, then we have applied them to model new set of two higher-order nonlinear partial differential equations which describe the dynamics of a coupled solitary wave in the given line. The construction of coupled solitary wave solutions of each set of modeled nonlinear partial differential equation by mathematical methods presented in [2][3][4][5][6][7][8][9][10][11][12][13][14][15] and new Bogning-Djeumen Tchaho-Kofane method presented in [16][17][18][19][20][21][22] has enabled us to obtain solitary wave solutions of type (Kink; Kink) and Solitary wave solution of type (Pulse; Pulse). The work we are presenting in this paper is partitioned as follows: in part 2, we present the general modeling of a modified Noguchi electrical line with crosslink capacitor, In part 3, we construct the solitary wave solution of type (Kink; Kink) of the obtained set of differential equations, in part 4, we construct the solitary wave solution of type (Pulse; Pulse) of the obtained set of differential equations, in part 5, we present graphical results for certain values of electrical line parameters.…”

Nonlinear Schrödingers equations with cubic nonlinearity: M-derivative soliton solutions by $\exp(-\Phi(\xi))$-Expansion method

“…Moreover, conformable fractional versions of some nonlinear system were investigate [2][3][4]. Thus, investigation of optical soliton with fractional time evolution, become very important due to its application in secure communication system of analog and digital signals, and to carry out hight speed data transmission over distance of several thousands of kilometers [5][6][7][8][9][10][11][12]. Recently, some effective integration methods have been used to construct exact solutions for PDEs, such as semi-inverse variational principe [21], the simplest equation approach [22], the first integral method [23], ansatz scheme [24] and the generalized tanh method [26] and so on.…”

(Kink; Kink; Kink; Kink) and (Pulse; Pulse; Pulse; Pulse) Solutions of a Set of Four Equations Modeled in a Nonlinear Hybrid Electrical Line with Crosslink Capacitor

“…The use of these definitions and the application of Kirchhoff laws to the circuit of nonlinear hybrid electrical line with crosslink capacitor has enabled us to model a set of four nonlinear partial differential equations which describe the dynamics of solitary waves in the line. To construct exact solitary wave solution of each set of four nonlinear partial differential equations, we have used the mathematical methods presented in [3][4][5][6][7][8][9][10][11][12][13][14][15][16] and particularly the Bogning-Djeumen Tchaho-Kofane method [17][18][19][20][21][22]. For one of the set of four nonlinear partial differential equations, we have obtained a solution which is a set of four solitary waves of type (Pulse; Pulse; Pulse; Pulse) and for the other we have obtained a solution which is a set of four solitary waves of type (Kink; Kink; Kink; Kink).…”