# Dynamics of Rogue Wave Excitation Pattern on Stripe Phase Backgrounds in a Two-component Bose-Einstein Condensate

## TL;DR

This paper investigates rogue wave patterns in a two-component Bose-Einstein condensate with pair-transition effects, revealing new excitation behaviors and quantization rules that differ from scalar systems.

## Contribution

It introduces the study of rogue wave excitations on stripe phase backgrounds in two-component BECs with pair-transition effects, uncovering novel patterns and quantization formulas.

## Key findings

- Rogue waves can exist on stripe phase backgrounds with cosine and sine wave components.
- Rogue wave peaks are lower and vary with wave period.
- Number of rogue waves follows a new quantization rule involving two integers.

## Abstract

We study rogue wave excitation pattern in a two-component Bose-Einstein condensate with pair-transition effects. The results indicate that rogue wave excitation can exist on a stripe phase background for which there are cosine and sine wave background in the two components respectively. The rogue wave peak can be much lower than the ones of scalar matter wave rogue waves, and varies with the wave period changing. Both rogue wave pattern and rogue wave number on temporal-spatial plane are much more abundant than the ones reported before. Furthermore, we prove that the rogue wave number can be $n (n+1)/2+m (m+1)/2$ (where $m,n $ are arbitrary non-negative integers), in contrast to $n(n+1)/2$ for scalar nonlinear Schr\"{o}dinger equation described systems. These results would enrich our knowledge on nonlinear excitations in multi-component Bose-Einstein condensate with transition coupling effects.