Linear coupling effect induced beating non-degenerate vector solitons

TL;DR

The paper addresses generating beating solitons in a two-component CNLS system by leveraging nondegenerate vector solitons of the integrable Manakov model. It constructs beating solitons through a transformation that combines nondegenerate Manakov solitons with linear self- and cross-coupling between orthogonal modes, yielding beating at a frequency $\omega=|2\Gamma+k_{1R}^2-l_{1R}^2|$ and spatial period $Z=2\pi/|2\Gamma+k_{1R}^2-l_{1R}^2|$, while the total intensity remains non-oscillatory. The study shows these beating solitons undergo elastic collisions, preserving their beating, and demonstrates control of beating via collisions with degenerate beating solitons, supported by detailed asymptotic analysis. The findings offer new insights for beating solitons in nonlinear optics and Bose-Einstein condensates, with potential extensions to media with variable nonlinearity or tunable coupling along $z$.

Abstract

In this paper, we propose an alternative approach to generate a new class of beating vector solitons. Unlike earlier procedures that use dark-bright or bright-dark soliton solutions to generate beating solitons, the method described here utilizes non-degenerate vector soliton solutions of the Manakov system. It involves linear superposition of such soliton solutions along with an intensity switching mechanism facilitated by cross-coupling between the optical modes. We find that the obtained beating solitons collide elastically with themselves and keep their beating feature unchanged after the collision. We also find that their beating nature can be controlled by allowing them to collide with degenerate beating solitons exhibiting energy-sharing collisions. The results presented in this work will provide new insights into beating solitons in Bose-Einstein condensates, nonlinear optics, and related areas of research.

Figures (5)

• Figure 1: Self ($\rho=0.25$) and cross ($\nu=0.7$) coupling induced beating non-degenerate fundamental soliton. Panels (a1)-(a3): $k_1=0.565$, $l_1=0.3$, $\alpha_1^{(1)}=0.44+0.51i$, and $\alpha_1^{(2)}=0.43+0.5i$. Panels (b1)-(b3): $k_1=0.425$, $l_1=0.3$, $\alpha_1^{(1)}=0.44+0.51i$, and $\alpha_1^{(2)}=0.43+0.5i$. Panels (c1)-(c3): $k_1=0.32$, $l_1=0.34$, $\alpha_1^{(1)}=0.55$, and $\alpha_1^{(2)}=0.45$.
• Figure 2: Non-degenerate fundamental soliton of the Manakov system in the absence of self ($\rho$) and cross ($\nu$) coupling effects. Panels (a1) and (a2): $k_1=0.565$, $l_1=0.3$, $\alpha_1^{(1)}=0.44+0.51i$, and $\alpha_1^{(2)}=0.43+0.5i$. Panels (b1) and (b2): $k_1=0.425$, $l_1=0.3$, $\alpha_1^{(1)}=0.44+0.51i$, and $\alpha_1^{(2)}=0.43+0.5i$. Panels (c1) and (c2): $k_1=0.32$, $l_1=0.34$, $\alpha_1^{(1)}=0.55$, and $\alpha_1^{(2)}=0.45$.
• Figure 3: A stationary degenerate vector bright soliton of the Manakov system in the absence of self and cross-coupling effect is shown here. The parameter values are $k_1=l_1=0.55$, $\alpha_1^{(1)}=0.5$, $\alpha_1^{(2)}=1$, and $\rho=\nu=0$.
• Figure 4: Beating-degenerate vector soliton: $\rho=0.25$, $\nu=0.7$, $k_1=l_1=0.55+0.5i$, $\alpha_1^{(1)}=0.5$, and $\alpha_1^{(2)}=1$.
• Figure 5: While panels (a1)-(a3) illustrate the elastic collision dynamics of two beating non-degenerate vector solitons, panels (b1)-(b3) depict how the beating effects of a non-degenerate soliton can be controlled through collision with a degenerate beating soliton. Panels (a1)-(a3): $\rho=0.25$, $\nu=0.8$, $k_1=0.565+0.8i$, $l_1=0.3+0.8i$, $k_2=0.3-i$, $l_2=0.57-i$, $\alpha_1^{(1)}=0.44+0.51i$, $\alpha_1^{(2)}=0.43+0.5i$, $\alpha_2^{(1)}=0.45+0.45i$, $\alpha_2^{(2)}=0.55$. Panels (b1)-(b3): $\rho=0.25$, $\nu=0.9$, $k_1=l_1=1.3+i$, $k_2=0.6-i$, $l_2=1.5-i$, $\alpha_1^{(1)}=0.5+0.5i$, $\alpha_1^{(2)}=0.5$, $\alpha_2^{(1)}=1$, $\alpha_2^{(2)}=0.45+0.6i$.