Investigation on the resonance phenomena of multi-solitons for the (3+1)-dimensional Kadomtsev–Petviashvili equation

doi:10.1088/1674-1056/20/1/015205

中国物理B ›› 2011, Vol. 20 ›› Issue (1): 15205-015205.doi: 10.1088/1674-1056/20/1/015205

• PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES • 上一篇下一篇

Investigation on the resonance phenomena of multi-solitons for the (3+1)-dimensional Kadomtsev–Petviashvili equation

石玉仁¹, 张娟¹, 杨红娟¹, 段文山¹, Karl E. Lonngren²

(1)College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, China; (2)Department of Electrical and Computer Engineering, The University of Iowa, Iowa City, IA 52242, USA

收稿日期:2010-06-04 修回日期:2010-07-22 出版日期:2011-01-15 发布日期:2011-01-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 10575082); the Key Project Foundation of the Education Ministry of China (Grant No. 209128), the Natural Science Foundation of Northwest Normal University (Grant No. NWNU-KJCXGC-03-53).

Investigation on the resonance phenomena of multi-solitons for the (3+1)-dimensional Kadomtsev–Petviashvili equation

Shi Yu-Ren(石玉仁)^a)†, Zhang Juan(张娟)^a), Yang Hong-Juan(杨红娟)^a), Duan Wen-Shan(段文山)^a), and Karl E. Lonngren^b)

^a College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, China; ^b Department of Electrical and Computer Engineering, The University of Iowa, Iowa City, IA 52242, USA

Received:2010-06-04 Revised:2010-07-22 Online:2011-01-15 Published:2011-01-15
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 10575082); the Key Project Foundation of the Education Ministry of China (Grant No. 209128), the Natural Science Foundation of Northwest Normal University (Grant No. NWNU-KJCXGC-03-53).

摘要/Abstract

摘要： In this paper, we theoretically investigate the four-soliton interaction and their resonance phenomena of the (3+1)-dimensional Kadomtsev--Petviashvili (KP) equation. We find that the maximum amplitude of the resonantly created soliton can be 16 times that of one of the four equi-amplitude initial interacting solitons. We also find that the maximum amplitude can only be 4 times the initial soliton amplitude when the resonance phenomena does not take place. The case of four solitons with different amplitudes also has been studied analytically. The results indicate that the resonance phenomena still exists in this case. Numerical results confirm the theoretical predictions.

Abstract: In this paper, we theoretically investigate the four-soliton interaction and their resonance phenomena of the (3+1)-dimensional Kadomtsev–Petviashvili (KP) equation. We find that the maximum amplitude of the resonantly created soliton can be 16 times that of one of the four equi-amplitude initial interacting solitons. We also find that the maximum amplitude can only be 4 times the initial soliton amplitude when the resonance phenomena does not take place. The case of four solitons with different amplitudes also has been studied analytically. The results indicate that the resonance phenomena still exists in this case. Numerical results confirm the theoretical predictions.

Key words: Kadomtsev–Petviashvili equation, soliton, resonance

中图分类号: (Solitons; BGK modes)

52.35.Sb

05.45.Yv (Solitons)

石玉仁, 张娟, 杨红娟, 段文山, Karl E. Lonngren. Investigation on the resonance phenomena of multi-solitons for the (3+1)-dimensional Kadomtsev–Petviashvili equation[J]. 中国物理B, 2011, 20(1): 15205-015205.

Shi Yu-Ren(石玉仁), Zhang Juan(张娟), Yang Hong-Juan(杨红娟), Duan Wen-Shan(段文山), and Karl E. Lonngren. Investigation on the resonance phenomena of multi-solitons for the (3+1)-dimensional Kadomtsev–Petviashvili equation[J]. Chin. Phys. B, 2011, 20(1): 15205-015205.

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Investigation on the resonance phenomena of multi-solitons for the (3+1)-dimensional Kadomtsev–Petviashvili equation

Investigation on the resonance phenomena of multi-solitons for the (3+1)-dimensional Kadomtsev–Petviashvili equation

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