Optical solitons with differential group delay for coupled Fokas–Lenells equation using two integration schemes

Soliton solutions to the B-type Kadomtsev–Petviashvili equation under general dispersion relations

The purpose of this study is to find some novel soliton solutions of Fokas–Lenells (FL) equation where the perturbation terms are taken into account with nonlinearity. The sine-Gordon expansion method (SGEM) and the $$(m+({G'}/{G}))$$
 -expansion method are used in this context. The dark, bright, dark–bright and singular optical soliton solutions are successfully obtained. Moreover, the constraint conditions for guaranteeing the existence of solutions are also given.

Optical soliton solutions to the Fokas-Lenells equation via sine-Gordon expansion method and (m +(G ' /G ) ) -expansion method

Chirp-free bright optical soliton perturbation with Chen–Lee–Liu equation by traveling wave hypothesis and semi-inverse variational principle

General dark solitons and mixed solutions consisting of dark solitons and breathers for the third-type Davey-Stewartson (DS-III) equation are derived by employing the bilinear method. By introducing the two differential operators, semi-rational solutions consisting of rogue waves, breathers, and solitons are generated. These semi-rational solutions are given in terms of determinants whose matrix elements have simple algebraic expressions. Under suitable parametric conditions, we derive general rogue wave solutions expressed in terms of rational functions. It is shown that the fundamental (simplest) rogue waves are line rogue waves. It is also shown that the multi-rogue waves describe interactions of several fundamental rogue waves, which would generate interesting curvy wave patterns. The higher order rogue waves originate from a localized lump and retreat back to it. Several types of hybrid solutions composed of rogue waves, breathers, and solitons have also been illustrated. Specifically, these semi-rational solutions have a new phenomenon: lumps form on dark solitons and gradual separation from the dark solitons is observed.

Semi-rational solutions of the third-type Davey-Stewartson equation.

In this paper, a vector generalization of the Fokas–Lenells system, which describes for nonlinear pulse propagation in optical fibers by retaining terms up to the next leading asymptotic order, is investigated. Higher-order soliton, breather, and rogue wave solutions of the coupled Fokas–Lenells system are derived via the n -fold Darboux transformation. Meanwhile the dynamic characteristics of those solitary wave solutions have been discussed.

J.W. Yang

Papers

Solitons, breathers and rogue waves for the coupled Fokas–Lenells system via Darboux transformation

The data acquisition algorithm designed for the SiPM-based detectors of GECAM satellite