2018
DOI: 10.1088/1674-1056/27/12/120202
|View full text |Cite
|
Sign up to set email alerts
|

N -soliton solutions for the nonlocal two-wave interaction system via the Riemann–Hilbert method

Abstract: In this paper, a nonlocal two-wave interaction system from the Manakov hierarchy is investigated via the Riemann-Hilbert approach. Based on the spectral analysis of the Lax pair, a Riemann-Hilbert problem for the nonlocal two-wave interaction system is constructed. By discussing the solutions of this Riemann-Hilbert problem in both the regular and nonregular cases, we explicitly present the N-soliton solution formula of the nonlocal two-wave interaction system. Moreover, the dynamical behaviour of the single-s… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
3
1
1

Citation Types

0
10
0

Year Published

2019
2019
2024
2024

Publication Types

Select...
7

Relationship

0
7

Authors

Journals

citations
Cited by 10 publications
(11 citation statements)
references
References 26 publications
0
10
0
Order By: Relevance
“…From the nature of trigonometric and exponential functions, we realize that there are an open bounded set D ∈ R × R + , 𝜌 > 0 and 𝜋 < ∞, such that the solutions (20), ( 24), (27), and (30) and their conformable derivatives in (13) are uniformly bounded on D ×  𝜋 (𝜌). Further, they continue on D and analytic on  𝜋 (𝜌).…”
Section: Stochastic Wave Solutions Of the Ekdv Equationmentioning
confidence: 99%
See 1 more Smart Citation
“…From the nature of trigonometric and exponential functions, we realize that there are an open bounded set D ∈ R × R + , 𝜌 > 0 and 𝜋 < ∞, such that the solutions (20), ( 24), (27), and (30) and their conformable derivatives in (13) are uniformly bounded on D ×  𝜋 (𝜌). Further, they continue on D and analytic on  𝜋 (𝜌).…”
Section: Stochastic Wave Solutions Of the Ekdv Equationmentioning
confidence: 99%
“…[4][5][6][7][8] The checking of accurate and rough solutions of nonlinear development conditions plays a critical activity in the investigation of nonlinear physical questions. Numerous accommodating strategies, for example, bilinear change strategy, 9 the adjusted Clarkson and Kruskal (CK) direct strategy, 10 the multiscale extension strategy, 11 the binary Bell polyno-mials strategy, 12 the Riemann-Hilbert strategy, 13 the surmised balance strategy, 14 and the overall improved Kudryashov strategy 15 have been introduced in the ongoing writing.…”
Section: Introductionmentioning
confidence: 99%
“…Moreover, we mention that a nonlocal two-wave interaction system associated with an easier 3×3 matrix spectral problem is investigated with the aid of the Riemann-Hilbert approach by [25]. Let us study (2) for the localized solutions; we simply suppose that the potentials u and v decay to zero sufficiently fast as 푥 㨀→ ±∞, and 휖 is taken to be positive without loss of generality.…”
Section: Direct Scattering Processmentioning
confidence: 99%
“…[2,11] The investigation of exact and approximate solutions of nonlinear evolution equations plays an important role in the study of nonlinear physical phenomena. Many helpful methods such as bilinear transformation method, [35] the modified Clarkson and Kruskal (CK) direct method, [39] the multi-scale expansion method, [33] the binary Bell polynomials method, [48] the Riemann-Hilbert method, [41] and the approximate symmetry method [28] have been presented in the recent literature. He and Wu [19] introduced a concise and straightforward method, called the Exp-function method, to obtain generalized soliton, periodic, and compacton-like solutions for many nonlinear PDEs.…”
Section: Introductionmentioning
confidence: 99%