Long-distance interactions between optical solitons with an oscillating structure

Abstract

In this letter, long-distance interactions between optical solitons with an oscillating structure are investigated. Analytic two-soliton solutions for the variable-coefficient nonlinear Schrödinger equation are obtained. Different from the elastic interactions reported previously, the interaction solitons are accompanied with an oscillating structure during their interactions. Reasons for long-distance interactions are discussed, and influences of the corresponding parameters are analyzed. Those studies may provide a new insight into the soliton interactions.

Higher-order-effects management of soliton interactions in the Hirota equation

“…(1) are constants, the solution (25) generates common two-soliton interactions [18]. To analyze how frequency affects soliton interactions, we consider symmetric input pulses with frequency duration as follows [49][50][51]:…”

“…Therefore, in this paper, we are devoted to investigate the interaction between two solitons described by the Hirota equation via the bilinear method. Generally speaking, the interaction force between two solitons can be repulsive or attractive, depending mainly on their relative phase [11,18,19]. Soliton interactions can be used in pulse compression, energy conversion, and amplification [20][21][22].…”

2D optical rogue waves in self-focusing Kerr-type media with spatially modulated coefficients

“…Theoretical studies have shown that the rogue wave phenomenon can be explained well by nonlinear theories [7], and various possible formative mechanisms have been explored, such as the modulation instability in one dimension (1D) [8], nonlinear spectral instability [9], and crossings in 2D [10,11]. Furthermore, the rogue wave phenomenon has been observed experimentally in a variety of physical systems, including optical fibers [12,13], water wave tanks [14], capillary waves [15], and plasma waves [5], leading to a better understanding of the conditions for appearance and general features of rogue waves.…”

Breathers and localized solutions of complex modified Korteweg–de Vries equation

“…[6][7][8][9][10][11][12] The analytical calculations of those soliton equations have been in the limelight in the research of the nonlinear science. [13][14][15][16][17][18][19][20][21][22][23] Currently, several powerful mathematical methods have been applied to solve the exact solution in the theory of solitons, such as the Darboux transformation (DT), inverse scattering method, Backlund transformation and the bilinear derivative method. [24][25][26][27][28][29][30][31][32][33] Breathers and localized solutions of complex MKdV equation…”