Riemann-Hilbert method and multi-soliton solutions of an extended modified Korteweg-de Vries equation with N distinct arbitrary-order poles

The Riemann-Hilbert (RH) method is developed to study the extended modified Korteweg-de Vries (emKdV) equation with zero boundary conditions. The analytical and asymptotic properties of Jost functions are obtained by the direct scattering analysis to establish a suitable RH problem. We consider the...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2022-07, Vol.511 (2), p.126103, Article 126103
Main Authors: Yang, Jin-Jie, Tian, Shou-Fu, Li, Zhi-Qiang
Format: Article
Language:English
Subjects:
N distinct poles
Riemann-Hilbert method
The extended modified Korteweg-de Vries equation
Zero boundary conditions
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Summary:The Riemann-Hilbert (RH) method is developed to study the extended modified Korteweg-de Vries (emKdV) equation with zero boundary conditions. The analytical and asymptotic properties of Jost functions are obtained by the direct scattering analysis to establish a suitable RH problem. We consider the singular RH problem of scattering data with N distinct poles. By using the generalized residue condition to solve the RH problem, we construct the exact solution of emKdV equation under the condition of no reflection. In addition, four kinds of special poles and their corresponding soliton solutions are discussed in detail, including one second-order pole, one third-order pole, three first-order poles and two second-order poles.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2022.126103