A Riemann-Hilbert Approach to Complex Sharma-Tasso-Olver Equation on Half Line

In this paper, the Fokas unified method is used to analyze the initial-boundary value problem of a complex Sharma-Tasso-Olver （cSTO） equation on the half line. We show that the solution can be expressed in terms of the solution of a Riemann-Hilbert problem. The relevant jump matrices are explicitly...

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Published in理论物理通讯：英文版 Vol. 67; no. 11; pp. 580 - 594
Main Author 张宁;夏铁成;胡贝贝
Format Journal Article
LanguageEnglish
Published 2017
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Summary:In this paper, the Fokas unified method is used to analyze the initial-boundary value problem of a complex Sharma-Tasso-Olver （cSTO） equation on the half line. We show that the solution can be expressed in terms of the solution of a Riemann-Hilbert problem. The relevant jump matrices are explicitly given in terms of the matrix-value spectral functions spectral functions {a（λ）, b（A）} and {A（λ）, B（λ）}, which depending on initial data uo（ x ） = u（ x, 0） and boundary data go（y） = u（0, y）, gl（y） = us（0, y）, g2（y） = uxx（0, y）. These spectral functions are not independent, they satisfy a global relation.
Bibliography:11-2592/O3
In this paper, the Fokas unified method is used to analyze the initial-boundary value problem of a complex Sharma-Tasso-Olver （cSTO） equation on the half line. We show that the solution can be expressed in terms of the solution of a Riemann-Hilbert problem. The relevant jump matrices are explicitly given in terms of the matrix-value spectral functions spectral functions {a（λ）, b（A）} and {A（λ）, B（λ）}, which depending on initial data uo（ x ） = u（ x, 0） and boundary data go（y） = u（0, y）, gl（y） = us（0, y）, g2（y） = uxx（0, y）. These spectral functions are not independent, they satisfy a global relation.
Ning Zhang 1,2 Tie-Cheng Xia 1 and Bei-Bei Hu 1,3（ 1Department of Mathematics, Shanghai University, Shanghai 200444, China 2Department of Basical Courses, Shandong University of Science and Technology, Taian 271019, China 3School of Mathematicas and Finance, Chuzhou University, Chuzhou 239000, China）
the cSTO equation, initial-boundary value problem, Riemann-Hilbert problem, jump matrix,Fokas unified method
ISSN:0253-6102