Chirped optical soliton perturbation of Fokas–Lenells equation with full nonlinearity

Abstract

The present paper focuses on the chirped soliton solutions of the Fokas-Lenells equation in the presence of perturbation terms. A complex envelope traveling-wave solution is used to reduce the governing equation to an ordinary differential equation (ODE). An auxiliary equation in the form of a first-order nonlinear ODE with six-degree terms is implemented as a solution method. Various types of chirped soliton solutions including bright, dark, kink and singular solitons are extracted. The associated chirp is also determined for each of these optical pulses. Restrictions for the validity of chirped soliton solutions are presented.

Solutions for a Generalized Type of the Fokas–Lenells Equation

“…Te extensive algebraic system is obtained because we have avoided the restriction on the coefcients of equation ( 1) mentioned in the introduction. Clearly, the model considered here is a generalization of the standard given by equation (2). With respect to the standard Fokas-Lenells equation (FLE), the authors in [2] have derived solutions using the Jacobi elliptic function.…”

“…Te standard Fokas-Lenells equation (equation ( 2)) was proposed a few years ago as an interesting model to study the dynamics of solitons used in some applications in communications theory, and several approaches for the respective study have been used. In [2], a special ordinary diferential equation is used for obtaining chirped solutions; in [3], the Lie symmetries approach join the extended G′/G-expansion method is used to obtain optical solitons; in [4], the Sine-Gordon expansion method is used to handle equation ( 2) and obtain exact solutions. A detailed description of equation ( 2) can be found in [2][3][4]; however, we can mention that A is considered as the velocity of dispersion, B is the velocity of dispersion space-temporal, C is the autophase of modulation, and D is the nonlinear dispersion.…”

“…In [2], a special ordinary diferential equation is used for obtaining chirped solutions; in [3], the Lie symmetries approach join the extended G′/G-expansion method is used to obtain optical solitons; in [4], the Sine-Gordon expansion method is used to handle equation ( 2) and obtain exact solutions. A detailed description of equation ( 2) can be found in [2][3][4]; however, we can mention that A is considered as the velocity of dispersion, B is the velocity of dispersion space-temporal, C is the autophase of modulation, and D is the nonlinear dispersion. In the right side of equation ( 2), H is the intermodal dispersion, F is a perturbation term that corresponds to selfsteepening efect, and G is a perturbation term that determines nonlinear dispersion again.…”

“…Other techniques can be found in references [14][15][16] and references therein. In this work, we use the improved tanh-coth method described in reference [13] to obtain solutions of equation ( 1) and in a particular case to equation (2), complementing in this way the set of solutions obtained, for instance in [2][3][4]. Te improved tanh-coth method is a generalization of the extended tanh-coth method [10], and the Kudryashov method [11], as well as the G′/G-expansion method used widely in the analysis of several nonlinear equations.…”

Cubic–quartic optical soliton perturbation and modulation instability analysis in polarization-controlled fibers for Fokas–Lenells equation

“…The employed integration schemes in the previous studies are sine-Gordon expansion method, Riccati equation method, mapping method, trial equation method, Kudryashov's method, semi-inverse variational principle, modified simple equation method, Laplace-Adomian decomposition method, auxiliary equation method and many others. For more details, readers are referred to references [7][8][9][10][11][12][13][14][15][16][17][18].…”