Kavli Affiliate: Feng Yuan
| First 5 Authors: Feng Yuan, Jingsong He, Yi Cheng, ,
| Summary:
The reconnection processes of 3-solitons with 2-resonance can produce
distinct local structures that initially connect two pairs of V-shaped
branches, then disappear, and later re-emerge as new forms. We call such local
structures as stem structures. In this paper, we investigate the
variable-length stem structures during the soliton reconnection of the
asymmetric Nizhnik-Novikov-Veselov system. We consider two scenarios: weak
2-resonances (i.e., $a_{12}=a_{13}=0,,0<a_{23}<+infty$) and strong
2-resonances (i.e., $a_{12}=a_{13}=+infty,,0<a_{23}<+infty$). We determine
the asymptotic forms of the four arms and their corresponding stem structures
using two-variable asymptotic analysis method which is involved simultaneously
with one space variable $y$ (or $x$) and one temporal variable $t$. Different
from known studies, our findings reveal that the asymptotic forms of the arms
$S_2$ and $S_3$ differ by a phase shift as $ttopminfty$. Building on these
asymptotic forms, we perform a detailed analysis of the trajectories,
amplitudes, and velocities of the soliton arms and stem structures.
Subsequently, we discuss the localization of the stem structures, focusing on
their endpoints, lengths, and extreme points in both weak and strong
2-resonance scenarios.
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