Modulation instability and localized wave excitations for a higher-order modified self-steepening nonlinear Schrödinger equation in nonlinear optics

Abstract

This paper investigates a higher-order modified nonlinear Schrödinger equation with higher-order dispersion and self-steepening effects, which can be used to study the dynamics of asymmetric and steepened optical pulse transmission in optical fibres. The modulation instability of the plane-wave solution has been analysed, and the state transition of the rogue waves under the higher-order dispersion effect is presented. The findings demonstrate that the self-steepening effect may also produce an asymmetric unstable frequency band. Combined with the modulation instability, the rogue wave, rational soliton and mixed interaction of localized waves have a quantitative relationship with plane-wave parameters. Various exact solutions can be accurately located and obtained according to the generalized Darboux transformation. The asymptotic analysis of rational solutions demonstrates the state transition of higher-order rogue waves. This paper illustrates the significance of modulation instability for studying the integrable systems by the Darboux transformation. It is a new guidance to solve the difficulty of exact excitation of asymmetric localized waves in complex integrable systems. The results have prospective applications and references for the emergence, amplification and compression of asymmetric pulses in optical experiments.

Multi-soliton solutions of coupled Lakshmanan–Porsezian–Daniel equations with variable coefficients under nonzero boundary conditions

“…When the coefficients σ (t) and γ 1 (t) are constants, we observe two distinct scenarios in Figs. 13 When the coefficients σ (t) and γ 1 (t) are quadratic or cubic functions, similar phenomena occur. Here, we only demonstrate the case of quadratic functions.…”

“…[6][7][8] When dealing with non-uniform optical fibers, employing variable-coefficient NLS-type models offers a more accurate characterization of the system compared to their constantcoefficient counterparts. [9][10][11][12] With these insights, we study a coupled variable-coefficient LPDE to delineate the concurrent propagation of nonlinear waves in non-uniform optical media, [13][14][15][16][17][18] iq j,t + σ (t)q j,xx + ζ (t)…”

“…Extensive researches have been investigated on Eq. (1) under zero boundary conditions: Hirota's method has been used to analyze the interaction between solitons; [13] generalized Darboux transformations (DT) have been employed to obtain rogue waves and solitons; [14] binary DT and Hirota methods have been utilized to identify soliton solutions, respectively; [15] breathers, multi-peak solitons, and the transition from breathers to solitons have been analyzed through DT; [16,17] multi-soliton solutions have been investigated via parameter modulation and asymptotic analysis. [18] As far as we know, there have been no reports on investigations of soliton solutions for the LPDE under nonzero boundary conditions (NZBC).…”

Three-Soliton Interactions and the Implementation of Their All-Optical Switching Function

“…On the other hand, in optical communication systems, in order to improve the bit rate, each optical soliton is input into the fiber at smaller intervals. [18][19][20][21] However, this can cause interactions between adjacent optical soli-tons, which can cause distortion of some optical solitons, leading to a decrease in the bandwidth of the optical communication system and weakening its communication capability. [22][23][24][25] In order to improve the communication capability of the system, it is necessary to study the interaction between optical solitons in the system.…”

Higher-Order Nonlinear Effects on Optical Soliton Propagation and Their Interactions

“…Therefore, rather than the standard form equation, the high-order NLSE (HNLSE) is required to express femtosecond optical solitons propagation in optical fibers mathematically. [28][29][30][31] In this Letter, taking the higher-order nonlinear effects into consideration, we analytically investigate the variable coefficient coupled high-order nonlinear Schrödinger equation (VCHNLSE) that can be used to describe the transmission of femtosecond optical solitons in optical fibers. The specific form of the equation is [32] 𝑖𝑞1,𝑡 + 𝑞1,𝑥𝑥…”