This paper obtains soliton solutions to optical couplers by two methods. These are sine–cosine function method and Bernoulli’s equation approach. There are four laws that are touched upon in this paper. These are Kerr law, power law, parabolic law and dual-power law. The first integration scheme is applicable to Kerr and power laws only where bright soliton solutions are retrievable. The second tool is applicable to parabolic and dual-power laws only that leads to dark and singular solitons for these two nonlinear media.

Optical solitons in nonlinear directional couplers by sine–cosine function method and Bernoulli’s equation approach

Exact traveling wave solutions to the fractional coupled nonlinear Schrodinger equations

Optical soliton perturbation with fractional-temporal evolution by first integral method with conformable fractional derivatives

For the exponential traveling wave solutions to the Hirota bilinear equations, a sufficient and necessary criterion for the existence of linear superposition principle has been given. Motivated by this criterion, we propose a new Hirota bilinear equation via using a multivariate polynomial. Applying the linear superposition principle to this new Hirota bilinear equation, we finally find two types of resonant multiple wave solutions, among which, the resonant three-wave solutions are illustrated with three-dimensional plots.

Resonant behavior of multiple wave solutions to a Hirota bilinear equation

This paper addresses the Biswas–Milovic equation as a generalized model for soliton propagation through optical wave guides. The extended trail equation method reveals several forms of soliton solution such as bright, dark and singular solitons. Other wave solutions fall out as by-product of this integration algorithm.

Optical solitons with Biswas–Milovic equation by extended trial equation method

This work addresses Thirring optical solitons in birefringent ?bers. The dynamics of the vector coupled nonlinear Schr?dinger equation, which describes the propagation of Thirring solitons through birefringent optical ?bers with spatio-temporal dispersion and Kerr law nonlinearity, is investigated analytically. The tools of integration applied in this dynamical model are the Jacobian elliptic equation?expansion approach, Riccati equation?expansion scheme and soliton ansatz method. These algorithms lead to exact Thirring bright, dark and singular solitons along with the corresponding parameter constraints.

https://iopscience.iop.org/article/10.1088/1054-660X/25/1/015402/pdf

Thirring optical solitons in birefringent ﬁbers with spatio-temporal dispersion and Kerr law nonlinearity

This work studies nonlinear dynamics of optical solitons in a cascaded system with Kerr law nonlinearity and spatio-temporal dispersion. The mathematical model that describes the propagation of optical solitons through a cascaded system is given by the vector-coupled nonlinear Schrodinger equation. It is investigated analytically using three integration algorithms. The Jacobian elliptic equation expansion method, Bernoulli equation expansion approach and Riccati equation expansion scheme are the integration tools of this model that are recruited to extract singular, bright and dark solitons. The restrictions that need to hold for the existence of these solitons are derived.

http://iopscience.iop.org/article/10.1088/1054-660X/25/2/025402/pdf

Bright, dark and singular optical solitons in a cascaded system

This work studies the propagation of optical solitons through nonlinear metamaterials in the presence of spatio-temporal dispersion, parabolic law nonlinearity (cubic–quintic nonlinearity), detuning, inter-modal dispersion, self-steepening, Raman effect, nonlinear dispersion and third-order dispersion. Two integration approaches that are the Riccati equation expansion method and the ansatz scheme are applied to extract exact solitons. Finally, analytical bright, dark as well as singular soliton solutions are reported along with their respective restrictions for the first time.

Exact optical solitons in metamaterials with cubic–quintic nonlinearity and third-order dispersion

In this paper a new type of combined optical solitons are derived in the weakly nonlocal nonlinear parabolic law medium for
the first time. The nonlocal nonlinear Schrodinger equation is investigated analytically. The combined bright-dark solitons
and the corresponding existence conditions are reported. The presented results have important applications in nonlinear
optics and Bose-Einstein condensates.

Bright-Dark combo optical solitons with non-local nonlinearity in parabolic law medium

The ultrashort pulse propagation in optical metamaterials (OMMs) modeled by a generalized nonlinear Schrodinger equation with higher order effects is studied, in the present paper. To this end, by considering a complex envelope and a specific nonlinear chirp ansatz, a wide range of exact chirped soliton solutions are derived in the presence of the pseudo-quintic nonlinearity and the self-steepening effect. Exact solutions include kink and anti-kink chirped soliton solutions that are retrieved through the use of newly well-designed methods. The complex envelopes presented herein provide new specific nonlinear shock wave structures in OMMs which are vital for numerical and experimental verifications.

Yaxian Liu

Papers

Thirring optical solitons in birefringent ﬁbers with spatio-temporal dispersion and Kerr law nonlinearity

Bright, dark and singular optical solitons in a cascaded system

Exact optical solitons in metamaterials with cubic–quintic nonlinearity and third-order dispersion

Bright-Dark combo optical solitons with non-local nonlinearity in parabolic law medium

Analytic study on chirped optical solitons in nonlinear metamaterials with higher order effects