A study of periodic solutions and periodic background solutions for the reverse-space-time modified nonlinear Schrodinger equation

The modified nonlinear Schrodinger (MNLS) equation is used to describe the effect of femtosecond pulses and nonlinear dispersion in long single-mode fibers and the propagation of modulated Alfven waves along a magnetic field in a cold plasma. Under investigation in this paper is its nonlocal reverse-space-time type, extending it to the more general case, which has much physical significance in the field of nonlocal non-linear dynamical systems. Through constructing nonlocal type Darboux transformations (DTs), we will derive a series of new solutions as follows: (1)Bright and dark solitons on plane wave backgrounds, single and double periodic solutions; (2)Breather, rogue wave solutions and their coexistence mechanism on single periodic backgrounds via odd-fold DTs; (3) Bright and dark breather-like solutions on single periodic backgrounds, breather, rogue wave solutions and their degenerate and coexistence forms on double periodic backgrounds via even-fold DTs. In addition, we will discuss dynamic behaviors of those solutions through graphic simulations. (c) 2023 Elsevier B.V. All rights reserved.

Automated summary

The modified nonlinear Schrodinger (MNLS) equation is used to describe the propagation of femtosecond pulses and modulated Alfven waves in different physical systems. By constructing nonlocal type Darboux transformations (DTs), several new solutions are derived, including bright and dark solitons, periodic solutions, breathers, and rogue wave solutions. The dynamic behaviors of these solutions are discussed through graphic simulations.