Breathers and Soliton Solutions for a Generalization of the Nonlinear Schrödinger Equation

Abstract

A generalized nonlinear Schrödinger equation, which describes the propagation of the femtosecond pulse in single mode optical silica fiber, is analytically investigated. By virtue of the Darboux transformation method, some new soliton solutions are generated: the bright one-soliton solution on the zero background, the dark one-soliton solution on the continuous wave background, the Akhmediev breather which delineates the modulation instability process, and the breather evolving periodically along the straight line with a certain angle ofx-axis andt-axis. Those results might be useful in the study of the femtosecond pulse in single mode optical silica fiber.

Exact Periodic Wave, Bisoliton, and Various Breather Solutions for the Zakharov Equations

“…Many rogue waves have been obtained [13][14][15][16][17][18]. Here we continue to analyze the rogue wave phenomenon and study the existence of rogue waves of (1).…”

Multisoliton Solutions and Breathers for the Coupled Nonlinear Schrödinger Equations via the Hirota Method

“…Even though (1), (2), and (3) may adequately describe the propagation in a single-mode waveguide, switching operations, and routing, other optical effects which involve soliton pulses require the interaction between two or more modes [13,14]. For several past decades, soliton propagation in the coupled nonlinear Schrödinger (CNLS) equations with different effective terms has been investigated from numerical simulation through applying Painlevé analysis [14], constructing Lax pair [15,16], and carrying on gauge transformation [17][18][19]. In particular, [20] reveals the ABand Ma-breathers and localized solitons for the Hirota-Maxwell-Bloch system on constant backgrounds in erbium doped fibers in detail.…”