MOLECULES AND NEW INTERACTIONAL STRUCTURES FOR A (2+1)-DIMENSIONAL GENERALIZED KONOPELCHENKO-DUBROVSKY-KAUP-KUPERSHMIDT EQUATION*

doi:10.1007/s10473-023-0106-7

数学物理学报(英文版) ›› 2023, Vol. 43 ›› Issue (1): 80-96.doi: 10.1007/s10473-023-0106-7

MOLECULES AND NEW INTERACTIONAL STRUCTURES FOR A (2+1)-DIMENSIONAL GENERALIZED KONOPELCHENKO-DUBROVSKY-KAUP-KUPERSHMIDT EQUATION^*

Yan Li¹, Ruoxia Yao^2,†, Yarong Xia²

1. School of Computer Science, Shaanxi Normal University, Xi'an 710119, China;
2. School of Information and Engineering, Xi'an University, Xi'an 710065, China

收稿日期:2021-09-06 修回日期:2022-06-23 发布日期:2023-03-01
通讯作者: †Ruoxia YAO.E-mail: rxyao@snnu.edu.cn
基金资助:
*National Natural Science Foundation of China (12001424), the Natural Science Basic Research Program of Shaanxi Province (2021JZ-21) and the Fundamental Research Funds for the Central Universities (2020CBLY013).

MOLECULES AND NEW INTERACTIONAL STRUCTURES FOR A (2+1)-DIMENSIONAL GENERALIZED KONOPELCHENKO-DUBROVSKY-KAUP-KUPERSHMIDT EQUATION^*

Yan Li¹, Ruoxia Yao^2,†, Yarong Xia²

1. School of Computer Science, Shaanxi Normal University, Xi'an 710119, China;
2. School of Information and Engineering, Xi'an University, Xi'an 710065, China

Received:2021-09-06 Revised:2022-06-23 Published:2023-03-01
Contact: †Ruoxia YAO.E-mail: rxyao@snnu.edu.cn
About author:Yan Li, E-mail: yanli@snnu.edu.cn; Yarong Xia, E-mail: xiayarong2014@126.com
Supported by:
*National Natural Science Foundation of China (12001424), the Natural Science Basic Research Program of Shaanxi Province (2021JZ-21) and the Fundamental Research Funds for the Central Universities (2020CBLY013).

摘要/Abstract

摘要： Soliton molecules (SMs) of the (2+1)-dimensional generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt (gKDKK) equation are found by utilizing a velocity resonance ansatz to $N$-soliton solutions, which can transform to asymmetric solitons upon assigning appropriate values to some parameters. Furthermore, a double-peaked lump solution can be constructed with breather degeneration approach. By applying a mixed technique of a resonance ansatz and conjugate complexes of partial parameters to multisoliton solutions, various kinds of interactional structures are constructed; There include the soliton molecule (SM), the breather molecule (BM) and the soliton-breather molecule (SBM). Graphical investigation and theoretical analysis show that the interactions composed of SM, BM and SBM are inelastic.

关键词: (2+1)-dimensional generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt equation, soliton molecules, velocity resonance, nonelastic interaction

Abstract: Soliton molecules (SMs) of the (2+1)-dimensional generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt (gKDKK) equation are found by utilizing a velocity resonance ansatz to $N$-soliton solutions, which can transform to asymmetric solitons upon assigning appropriate values to some parameters. Furthermore, a double-peaked lump solution can be constructed with breather degeneration approach. By applying a mixed technique of a resonance ansatz and conjugate complexes of partial parameters to multisoliton solutions, various kinds of interactional structures are constructed; There include the soliton molecule (SM), the breather molecule (BM) and the soliton-breather molecule (SBM). Graphical investigation and theoretical analysis show that the interactions composed of SM, BM and SBM are inelastic.

Key words: (2+1)-dimensional generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt equation, soliton molecules, velocity resonance, nonelastic interaction

Yan Li, Ruoxia Yao, Yarong Xia. MOLECULES AND NEW INTERACTIONAL STRUCTURES FOR A (2+1)-DIMENSIONAL GENERALIZED KONOPELCHENKO-DUBROVSKY-KAUP-KUPERSHMIDT EQUATION^*[J]. 数学物理学报(英文版), 2023, 43(1): 80-96.

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MOLECULES AND NEW INTERACTIONAL STRUCTURES FOR A (2+1)-DIMENSIONAL GENERALIZED KONOPELCHENKO-DUBROVSKY-KAUP-KUPERSHMIDT EQUATION^*

MOLECULES AND NEW INTERACTIONAL STRUCTURES FOR A (2+1)-DIMENSIONAL GENERALIZED KONOPELCHENKO-DUBROVSKY-KAUP-KUPERSHMIDT EQUATION^*

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