Certain bright soliton interactions of the Sasa-Satsuma equation in a monomode optical fiber

Abstract

Under investigation in this paper is the Sasa-Satsuma equation, which describes the propagation of ultrashort pulses in a monomode fiber with the third-order dispersion, self-steepening, and stimulated Raman scattering effects. Based on the known bilinear forms, through the modified expanded formulas and symbolic computation, we construct the bright two-soliton solutions. Through classifying the interactions under different parameter conditions, we reveal six cases of interactions between the two solitons via an asymptotic analysis. With the help of the analytic and graphic analysis, we find that such interactions are different from those of the nonlinear Schrödinger equation and Hirota equation. When those solitons interact with each other, the singular-I soliton is shape-preserving, while the singular-II and nonsingular solitons may be shape preserving or shape changing. Such elastic and inelastic interaction phenomena in a scalar equation might enrich the knowledge of soliton behavior, which could be expected to be experimentally observed.

An Analytical Scheme for the Analysis of Multi-Hump Solitons

“…The properties of classical soliton solutions with imposed symmetry and nonsingularity constraints are investigated. Due to the structure and properties of perfect solitons, the given analytical framework provides a solid foundation for the investigation of multi-hump soliton solutions to nonlinear models describing optical pulse propagations in optical¯bers, since it is well known that multi-hump solitons exists can propagate through such¯bers [12,24].…”

“…Let x; y satisfy conditions (36), (37). Then it is clear that (35) is a double-hump soliton solution which has potential applications in the¯eld of optical pulse propagation through optical¯bers [12]. The main idea of this technique is to insert (35) into ((33), (34)) and solve the resulting algebraic equations for the parameters of the system.…”

“…Double-hump soliton solution to systems of di®erential equations that have concrete applications in optics have already been constructed. In [12], Liu et al demonstrate that the Sasa-Satsuma equation, which is used to model propagation of ultrashort pulses in a monomode¯ber, admits double-hump soliton solutions. The stability of double-hump solitons in a medium with periodic modulation of nonlinear e®ects is studied in [9].…”

Darboux transformation of a two‐component generalized Sasa–Satsuma equation and explicit solutions

“…This equation is an integrable higher order NLS equation and has been proved to have many important applications in physics. For example, it appears in the description of ultrashort pulse propagation in optical fibers 14,15 . The Sasa–Satsuma equation has been widely studied by the Hirota bilinear method, 12,16 inverse scattering transform, 17,18 Darboux transformation, 13,19–21 Riemann‐Hilbert approach, 22–24 and others 25–28 in the past two decades.…”

“…For example, it appears in the description of ultrashort pulse propagation in optical fibers. 14,15 The Sasa-Satsuma equation has been widely studied by the Hirota bilinear method, 12,16 inverse scattering transform, 17,18 Darboux transformation, 13,[19][20][21] Riemann-Hilbert approach, [22][23][24] and others [25][26][27][28] in the past two decades. Some important explicit solutions related to the Sasa-Satsuma equation have been found.…”