Modulated equations of Hamiltonian PDEs and dispersive shocks
| Autor: | Benzoni-Gavage, Sylvie, Mietka, Colin, Rodrigues, L. Miguel |
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| Rok vydání: | 2019 |
| Předmět: | |
| Zdroj: | Nonlinearity, 34, No. 1, pp. 578--641 (2021) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1088/1361-6544/abcb0a |
| Popis: | Motivated by the ongoing study of dispersive shock waves in non integrable systems, we propose and analyze a set of wave parameters for periodic waves of a large class of Hamiltonian partial differential systems -- including the generalized Korteweg de Vries equations and the Euler-Korteweg systems -- that are well-behaved in both the small amplitude and small wavelength limits. We use this parametrization to determine fine asymptotic properties of the associated modulation systems, including detailed descriptions of eigenmodes. As a consequence, in the solitary wave limit we prove that modulational instability is decided by the sign of the second derivative -- with respect to speed, fixing the endstate -- of the Boussinesq moment of instability; and, in the harmonic limit, we identify an explicit modulational instability index, of Benjamin--Feir type. Comment: 65 pages |
| Databáze: | arXiv |
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