Initial value problem and soliton solutions of the single-cycle short pulse equation via the Riemann-Hilbert approach

被引：8

作者：

Bo, Ge-Qiang ^{[1
]}

Zhang, Wei-Guo ^{[1
]}

机构：

[1] Univ Shanghai Sci & Technol, Coll Sci, Shanghai 200093, Peoples R China

来源：

JOURNAL OF PHYSICS COMMUNICATIONS | 2018年 / 2卷 / 11期

基金：

中国国家自然科学基金;

关键词：

single-cycle short pulse equation; initial value problem; Riemann-Hilbert problem;

D O I：

10.1088/2399-6528/aaeaf5

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

This paper solves the initial value problem of the single-cycle short pulse equation u(xt) = u + 1/2u(u(2))(xx) via the Riemann-Hilbert approach. By converting initial value problem into the Riemnn-Hilbert problem, we have obtained one-soliton solutions and two-soliton solutions for the single-cycle short pulse equation.

引用

页数：11

共 22 条

[1] On a Riemann-Hilbert problem for the Fokas-Lenells equation
Ai, Liping
Xu, Jian
[J]. APPLIED MATHEMATICS LETTERS, 2019, 87 : 57 - 63
[2] The bi-Hamiltonian structure of the short pulse equation
Brunelli, J. C.
[J]. PHYSICS LETTERS A, 2006, 353 (06) : 475 - 478
[3] The short pulse hierarchy
Brunelli, JC
[J]. JOURNAL OF MATHEMATICAL PHYSICS, 2005, 46 (12)
[4] Ultra-short pulses in linear and nonlinear media
Chung, Y
Jones, CKRT
Schäfer, T
Wayne, CE
[J]. NONLINEARITY, 2005, 18 (03) : 1351 - 1374
[5] The short pulse equation by a Riemann-Hilbert approach
de Monvel, Anne Boutet
Shepelsky, Dmitry
Zielinski, Lech
[J]. LETTERS IN MATHEMATICAL PHYSICS, 2017, 107 (07) : 1345 - 1373
[6] Riemann-Hilbert approach and N-soliton solutions for a generalized Sasa-Satsuma equation
Geng, Xianguo
Wu, Jianping
[J]. WAVE MOTION, 2016, 60 : 62 - 72
[7] Guo B, 2018, APPL ANAL
[8] A Riemann-Hilbert approach for a new type coupled nonlinear Schrodinger equations
Guo, Boling
Liu, Nan
Wang, Yufeng
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2018, 459 (01) : 145 - 158
[9] Hone A, 2018, LETT MATH PHYS, V108, P1
[10] Solvability of singular integro-differential equations via Riemann-Hilbert problem
Li, Pingrun
Ren, Guangbin
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2018, 265 (11) : 5455 - 5471

← 1 2 3 →