Modulational instability and decomposition of nonlinear localized waves for the principal chiral field equation

Abstract

In this paper, we focus on the principal chiral field equation possessing the features of asymptotic freedom and dimensional transmutation, which may characterize the chiral properties of particles. Firstly, we analyze the modulational instability based on plane wave solutions. Secondly, we develop the iterative generalized $(n,N-n)$-fold Darboux transformation for this model to obtain rogue waves, periodic waves and their interaction states. Moreover, the higher-order rogue waves can be separated into multiple simple rogue waves, and the central locations of these simple rogue waves form triangles, pentagons and other shapes. Then, the movements and decomposition mechanisms of rogue waves on the constant backgrounds are studied with the large-parameter asymptotic analysis technique. We find that rogue waves can be separated along specific trajectories. Finally, the motion trajectories and distributions of magnetic vector and self-consistent potential are also taken into account. In contrast to other regions, the area where rogue waves are excited can cause remarkable changes in direction of magnetic vector and self-consistent potential. Our findings may contribute to understand the nonlinear localized waves in associated fields.