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A coupling problem for entire functions and its application to the long-time asymptotics of integrable wave equations
We propose a novel technique for analysing the long-time asymptotics of integrable wave equations in the case when the underlying isospectral problem has a purely discrete spectrum. To this end, we introduce a natural coupling problem for entire functions, which serves as a replacement for the usual...
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| Format: | Default Article |
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2016
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| Online Access: | https://hdl.handle.net/2134/35148 |
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| _version_ | 1818169284322394112 |
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| author | Jonathan Eckhardt Gerald Teschl |
| author_facet | Jonathan Eckhardt Gerald Teschl |
| author_sort | Jonathan Eckhardt (5731769) |
| collection | Figshare |
| description | We propose a novel technique for analysing the long-time asymptotics of integrable wave equations in the case when the underlying isospectral problem has a purely discrete spectrum. To this end, we introduce a natural coupling problem for entire functions, which serves as a replacement for the usual Riemann–Hilbert problem, which does not apply in these cases. As a prototypical example, we investigate the long-time asymptotics of the dispersionless Camassa–Holm equation. |
| format | Default Article |
| id | rr-article-9384875 |
| institution | Loughborough University |
| publishDate | 2016 |
| record_format | Figshare |
| spelling | rr-article-93848752016-02-04T00:00:00Z A coupling problem for entire functions and its application to the long-time asymptotics of integrable wave equations Jonathan Eckhardt (5731769) Gerald Teschl (7160909) Other mathematical sciences not elsewhere classified Coupling problem Long-time asymptotics Camassa–Holm equation Mathematical Sciences not elsewhere classified We propose a novel technique for analysing the long-time asymptotics of integrable wave equations in the case when the underlying isospectral problem has a purely discrete spectrum. To this end, we introduce a natural coupling problem for entire functions, which serves as a replacement for the usual Riemann–Hilbert problem, which does not apply in these cases. As a prototypical example, we investigate the long-time asymptotics of the dispersionless Camassa–Holm equation. 2016-02-04T00:00:00Z Text Journal contribution 2134/35148 https://figshare.com/articles/journal_contribution/A_coupling_problem_for_entire_functions_and_its_application_to_the_long-time_asymptotics_of_integrable_wave_equations/9384875 CC BY 3.0 |
| spellingShingle | Other mathematical sciences not elsewhere classified Coupling problem Long-time asymptotics Camassa–Holm equation Mathematical Sciences not elsewhere classified Jonathan Eckhardt Gerald Teschl A coupling problem for entire functions and its application to the long-time asymptotics of integrable wave equations |
| title | A coupling problem for entire functions and its application to the long-time asymptotics of integrable wave equations |
| title_full | A coupling problem for entire functions and its application to the long-time asymptotics of integrable wave equations |
| title_fullStr | A coupling problem for entire functions and its application to the long-time asymptotics of integrable wave equations |
| title_full_unstemmed | A coupling problem for entire functions and its application to the long-time asymptotics of integrable wave equations |
| title_short | A coupling problem for entire functions and its application to the long-time asymptotics of integrable wave equations |
| title_sort | coupling problem for entire functions and its application to the long-time asymptotics of integrable wave equations |
| topic | Other mathematical sciences not elsewhere classified Coupling problem Long-time asymptotics Camassa–Holm equation Mathematical Sciences not elsewhere classified |
| url | https://hdl.handle.net/2134/35148 |