The elliptic sinh-Gordon equation in a semi-strip
We study the elliptic sinh-Gordon equation posed in a semi-strip by applying the so-called Fokas method, a generalization of the inverse scattering transform for boundary value problems. Based on the spectral analysis for the Lax pair formulation, we show that the spectral functions can be character...
| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2017-06-01
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| Series: | Advances in Nonlinear Analysis |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/anona-2016-0206 |
| _version_ | 1818586491242151936 |
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| author | Hwang Guenbo |
| author_facet | Hwang Guenbo |
| author_sort | Hwang Guenbo |
| collection | DOAJ |
| description | We study the elliptic sinh-Gordon equation posed in a
semi-strip by applying the so-called Fokas method, a
generalization of the inverse scattering transform for boundary
value problems. Based on the spectral analysis for the Lax pair
formulation, we show that the spectral functions can be
characterized from the boundary values.
We express the solution of the equation
in terms of the unique solution of the matrix Riemann–Hilbert problem
whose jump matrices are defined by the
spectral functions. Moreover, we
derive the global algebraic relation that involves the boundary
values. In addition, it can be verified that the solution of the
elliptic sinh-Gordon equation posed in the semi-strip exists if
the spectral functions defined by the boundary values satisfy this
global relation. |
| first_indexed | 2024-12-16T08:53:48Z |
| format | Article |
| id | doaj.art-c07663e254a84485959de0d698d0d1ef |
| institution | Directory Open Access Journal |
| issn | 2191-9496 2191-950X |
| language | English |
| last_indexed | 2024-12-16T08:53:48Z |
| publishDate | 2017-06-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Advances in Nonlinear Analysis |
| spelling | doaj.art-c07663e254a84485959de0d698d0d1ef2022-12-21T22:37:21ZengDe GruyterAdvances in Nonlinear Analysis2191-94962191-950X2017-06-018153354410.1515/anona-2016-0206anona-2016-0206The elliptic sinh-Gordon equation in a semi-stripHwang Guenbo0Department of Mathematics, Daegu University, GyeongsanGyeongbuk 38453, Republic of KoreaWe study the elliptic sinh-Gordon equation posed in a semi-strip by applying the so-called Fokas method, a generalization of the inverse scattering transform for boundary value problems. Based on the spectral analysis for the Lax pair formulation, we show that the spectral functions can be characterized from the boundary values. We express the solution of the equation in terms of the unique solution of the matrix Riemann–Hilbert problem whose jump matrices are defined by the spectral functions. Moreover, we derive the global algebraic relation that involves the boundary values. In addition, it can be verified that the solution of the elliptic sinh-Gordon equation posed in the semi-strip exists if the spectral functions defined by the boundary values satisfy this global relation.https://doi.org/10.1515/anona-2016-0206boundary value problemselliptic pdessinh-gordon equationintegrable equations47k15 35q55 |
| spellingShingle | Hwang Guenbo The elliptic sinh-Gordon equation in a semi-strip Advances in Nonlinear Analysis boundary value problems elliptic pdes sinh-gordon equation integrable equations 47k15 35q55 |
| title | The elliptic sinh-Gordon equation in a semi-strip |
| title_full | The elliptic sinh-Gordon equation in a semi-strip |
| title_fullStr | The elliptic sinh-Gordon equation in a semi-strip |
| title_full_unstemmed | The elliptic sinh-Gordon equation in a semi-strip |
| title_short | The elliptic sinh-Gordon equation in a semi-strip |
| title_sort | elliptic sinh gordon equation in a semi strip |
| topic | boundary value problems elliptic pdes sinh-gordon equation integrable equations 47k15 35q55 |
| url | https://doi.org/10.1515/anona-2016-0206 |
| work_keys_str_mv | AT hwangguenbo theellipticsinhgordonequationinasemistrip AT hwangguenbo ellipticsinhgordonequationinasemistrip |