Resonant multiple wave solutions to some integrable soliton equations

doi:10.1088/1674-1056/ab4d47

中国物理B ›› 2019, Vol. 28 ›› Issue (11): 110202-110202.doi: 10.1088/1674-1056/ab4d47

Resonant multiple wave solutions to some integrable soliton equations

Jian-Gen Liu(刘建根), Xiao-Jun Yang(杨小军), Yi-Ying Feng(冯忆颖)

1 School of Mathematics, China University of Mining and Technology, Xuzhou 221116, China;
2 State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou 221116, China;
3 School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou 221116, China

收稿日期:2019-08-21 修回日期:2019-09-18 出版日期:2019-11-05 发布日期:2019-11-05
通讯作者: Xiao-Jun Yang E-mail:xjyang@cumt.edu.cn
基金资助:
Project supported by the Yue-Qi Scholar of the China University of Mining and Technology (Grant No. 102504180004) and the 333 Project of Jiangsu Province, China (Grant No. BRA2018320).

Resonant multiple wave solutions to some integrable soliton equations

Jian-Gen Liu(刘建根)^1,2, Xiao-Jun Yang(杨小军)^1,2,3, Yi-Ying Feng(冯忆颖)^2,3

1 School of Mathematics, China University of Mining and Technology, Xuzhou 221116, China;
2 State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou 221116, China;
3 School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou 221116, China

Received:2019-08-21 Revised:2019-09-18 Online:2019-11-05 Published:2019-11-05
Contact: Xiao-Jun Yang E-mail:xjyang@cumt.edu.cn
Supported by:
Project supported by the Yue-Qi Scholar of the China University of Mining and Technology (Grant No. 102504180004) and the 333 Project of Jiangsu Province, China (Grant No. BRA2018320).

摘要/Abstract

摘要： To transform the exponential traveling wave solutions to bilinear differential equations, a sufficient and necessary condition is proposed. Motivated by the condition, we extend the results to the (2+1)-dimensional Kadomtsev-Petviashvili (KP) equation, the (3+1)-dimensional generalized Kadomtsev-Petviashvili (g-KP) equation, and the B-type Kadomtsev-Petviashvili (BKP) equation. Aa a result, we obtain some new resonant multiple wave solutions through the parameterization for wave numbers and frequencies via some linear combinations of exponential traveling waves. Finally, these new resonant type solutions can be displayed in graphs to illustrate the resonant behaviors of multiple wave solutions.

关键词: linear superposition principle, resonant multiple wave solutions, (2+1)-dimensional Kadomtsev-Petviashvili (KP) equation, (3+1)-dimensional g-KP and BKP equations

Abstract: To transform the exponential traveling wave solutions to bilinear differential equations, a sufficient and necessary condition is proposed. Motivated by the condition, we extend the results to the (2+1)-dimensional Kadomtsev-Petviashvili (KP) equation, the (3+1)-dimensional generalized Kadomtsev-Petviashvili (g-KP) equation, and the B-type Kadomtsev-Petviashvili (BKP) equation. Aa a result, we obtain some new resonant multiple wave solutions through the parameterization for wave numbers and frequencies via some linear combinations of exponential traveling waves. Finally, these new resonant type solutions can be displayed in graphs to illustrate the resonant behaviors of multiple wave solutions.

Key words: linear superposition principle, resonant multiple wave solutions, (2+1)-dimensional Kadomtsev-Petviashvili (KP) equation, (3+1)-dimensional g-KP and BKP equations

中图分类号: (Integrable systems)

02.30.Ik

02.60.Cb (Numerical simulation; solution of equations) 02.70.Wz (Symbolic computation (computer algebra))

刘建根, 杨小军, 冯忆颖. Resonant multiple wave solutions to some integrable soliton equations[J]. 中国物理B, 2019, 28(11): 110202-110202.

Jian-Gen Liu(刘建根), Xiao-Jun Yang(杨小军), Yi-Ying Feng(冯忆颖). Resonant multiple wave solutions to some integrable soliton equations[J]. Chin. Phys. B, 2019, 28(11): 110202-110202.

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Resonant multiple wave solutions to some integrable soliton equations

Resonant multiple wave solutions to some integrable soliton equations

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