Periodic Travelling Wave Solutions of Discrete Nonlinear Schrödinger Equations
The existence of nonzero periodic travelling wave solutions for a general discrete nonlinear Schrödinger equation (DNLS) on one-dimensional lattices is proved. The DNLS features a general nonlinear term and variable range of interactions going beyond the usual nearest-neighbour interaction. The prob...
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2017/3694103 |
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| _version_ | 1850234561684832256 |
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| author | Dirk Hennig |
| author_facet | Dirk Hennig |
| author_sort | Dirk Hennig |
| collection | DOAJ |
| description | The existence of nonzero periodic travelling wave solutions for a general discrete nonlinear Schrödinger equation (DNLS) on one-dimensional lattices is proved. The DNLS features a general nonlinear term and variable range of interactions going beyond the usual nearest-neighbour interaction. The problem of the existence of travelling wave solutions is converted into a fixed point problem for an operator on some appropriate function space which is solved by means of Schauder’s Fixed Point Theorem. |
| format | Article |
| id | doaj-art-1673ff65f4c84818a5d000054dc56c92 |
| institution | OA Journals |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-1673ff65f4c84818a5d000054dc56c922025-08-20T02:02:37ZengWileyJournal of Applied Mathematics1110-757X1687-00422017-01-01201710.1155/2017/36941033694103Periodic Travelling Wave Solutions of Discrete Nonlinear Schrödinger EquationsDirk Hennig0Institut für Physik, Humboldt Universität zu Berlin, Erich-Steinfurth-Str. 10/11, 16227 Eberswalde, GermanyThe existence of nonzero periodic travelling wave solutions for a general discrete nonlinear Schrödinger equation (DNLS) on one-dimensional lattices is proved. The DNLS features a general nonlinear term and variable range of interactions going beyond the usual nearest-neighbour interaction. The problem of the existence of travelling wave solutions is converted into a fixed point problem for an operator on some appropriate function space which is solved by means of Schauder’s Fixed Point Theorem.http://dx.doi.org/10.1155/2017/3694103 |
| spellingShingle | Dirk Hennig Periodic Travelling Wave Solutions of Discrete Nonlinear Schrödinger Equations Journal of Applied Mathematics |
| title | Periodic Travelling Wave Solutions of Discrete Nonlinear Schrödinger Equations |
| title_full | Periodic Travelling Wave Solutions of Discrete Nonlinear Schrödinger Equations |
| title_fullStr | Periodic Travelling Wave Solutions of Discrete Nonlinear Schrödinger Equations |
| title_full_unstemmed | Periodic Travelling Wave Solutions of Discrete Nonlinear Schrödinger Equations |
| title_short | Periodic Travelling Wave Solutions of Discrete Nonlinear Schrödinger Equations |
| title_sort | periodic travelling wave solutions of discrete nonlinear schrodinger equations |
| url | http://dx.doi.org/10.1155/2017/3694103 |
| work_keys_str_mv | AT dirkhennig periodictravellingwavesolutionsofdiscretenonlinearschrodingerequations |