Elastic collisions of solitons generally have a finite phase shift. When the phase shift has a finitely large value, the two vertices of the (2 + 1)-dimensional two-soliton are significantly separated due to the phase shift, accompanied by the formation of a local structure connecting the two V-shaped solitons. We define this local structure as the stem structure. This study systematically investigates the localized stem structures between two solitons in the (2 + 1)-dimensional asymmetric Nizhnik–Novikov–Veselov system. These stem structures, arising from quasi-resonant collisions between the solitons, exhibit distinct features of spatial locality and temporal invariance. We explore two scenarios: one characterized by weakly quasi-resonant collisions (i.e. a12 ≈ 0), and the other by strongly quasi-resonant collisions (i.e. a12 ≈ +∞). Through mathematical analysis, we extract comprehensive insights into the trajectories, amplitudes, and velocities of the soliton arms. Furthermore, we discuss the characteristics of the stem structures, including their length and extreme points. Our findings shed new light on the interaction between solitons in the (2 + 1)-dimensional asymmetric Nizhnik–Novikov–Veselov system.
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August 2024
Research Article|
August 14 2024
Localized stem structures in quasi-resonant two-soliton solutions for the asymmetric Nizhnik–Novikov–Veselov system
Feng Yuan
;
Feng Yuan
(Data curation, Formal analysis, Investigation, Resources, Writing – original draft)
1
College of Science, Nanjing University of Posts and Telecommunications
, Nanjing 210023, People’s Republic of China
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Jiguang Rao;
Jiguang Rao
(Formal analysis, Project administration, Resources, Writing – review & editing)
2
School of Mathematics and Statistics, Hubei University of Science and Technology
, Xianning 437100, People’s Republic of China
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Jingsong He
;
Jingsong He
a)
(Project administration, Resources, Writing – review & editing)
3
Institute for Advanced Study, Shenzhen University
, Shenzhen 518060, People’s Republic of China
a)Author to whom correspondence should be addressed: hejingsong@szu.edu.cn
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Yi Cheng
Yi Cheng
(Project administration, Supervision, Writing – review & editing)
4
School of Mathematical Sciences, USTC
, Hefei, Anhui 230026, People’s Republic of China
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a)Author to whom correspondence should be addressed: hejingsong@szu.edu.cn
J. Math. Phys. 65, 083508 (2024)
Article history
Received:
May 12 2024
Accepted:
July 22 2024
Citation
Feng Yuan, Jiguang Rao, Jingsong He, Yi Cheng; Localized stem structures in quasi-resonant two-soliton solutions for the asymmetric Nizhnik–Novikov–Veselov system. J. Math. Phys. 1 August 2024; 65 (8): 083508. https://doi.org/10.1063/5.0218541
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