Nondegenerate solitons for coupled higher-order nonlinear Schrödinger equations in optical fibers

Abstract

Nondegenerate solitons have been demonstrated in recent years that they potentially allow a further increase of information transmission rates in optical communication due to their stable double-hump structures. In this paper, the femtosecond nondegenerate solitons in optical fibers which are described by the coupled higher-order nonlinear Schrödinger equations, are investigated. Analytical nondegenerate soliton solutions are constructed by the developing Hirota method. And the constraints for stable double-hump structures are put forward. Furthermore, soliton molecules and asymmetric solitons are also found as the new types of nondegenerate solitons. The interactions between two nondegenerate solitons are studied in their propagation.

Nondegenerate solitons of the (2+1)-dimensional coupled nonlinear Schrödinger equations with variable coefficients in nonlinear optical fibers

“…Inspired by the developing Hirota bilinear method applied to above-mentioned CNLS equations, [15,21] one may expand g 1 , g 2 and f as the power series expansions…”

“…Later, inspired by nondegenerate solitons, more general nondegenerate Kuznetsov-Ma breathers [12] and nondegenerate Akhmediev breathers [13,14] have also been studied. In recent years, based on several different mathematical physics methods such as the Hirota bilinear method, Kadomtsev-Petviashvili hierarchy reduction and developing Darboux transformation method, nondegenerate solitons have been reported in various multi-mode fiber systems, such as the Manakov systems, [15][16][17] generalized coupled nonlinear Schrödinger systems, [18][19][20][21][22] long-wave shortwave resonant interaction systems, [23] and coupled Fokas-Lenells systems. [24] Generally speaking, to describe the propagation of beams in two polarized directions, coupled nonlinear Schrödinger (CNLS) equations [25] iu z + 1 2 u tt + (|u| 2 + |v| 2 )u = 0, (1a)…”

Residual symmetries, consistent-Riccati-expansion integrability, and interaction solutions of a new (3+1)-dimensional generalized Kadomtsev-Petviashvili equation

“…For the new model, the Painlevé integrability, bilinear form, multiple-soliton and lump solutions are investigated, while the interaction wave solutions are unsolved. It is well known that several systematic methods to construct exact and analytical solutions have been proposed, including inverse scattering method, [23,24] Hirota bilinear method, [25][26][27][28][29][30] and Lie group analysis. [31] The purpose of this paper stems from the observation of interaction waves in laboratory experiments, such as Fermionic quantum plasma [32] and elastic woodpile periodic structures.…”

All-Optical Switches for Optical Soliton Interactions in a Birefringent Fiber

“…[21][22][23][24][25] In this Letter, we theoretically study the coupled nonlinear Schrödinger (CNLS) equation system, analyze the principle and properties of birefringent fiber optical soliton all-optical switching, and systematically explore the influence of various parameters on birefringent optical soliton all-optical switching. The CNLS equation can be written as [26,27] 𝑖𝑞𝑗,𝑡 + 𝑖𝑐0(𝑡)𝑞𝑗,𝑥 − 𝑘2(𝑡)…”

“…( 1) becomes an ordinary coupled NLS equation, which has been studied extensively before. [26] However, when 𝑘3(𝑡), 𝛾(𝑡), and 𝛾s(𝑡) are not equal to zero, the interaction characteristics of optical solitons have not been studied.…”