Numerical study of the transverse stability of line solitons of the Zakharov-Kuznetsov equations

Autor: Christian Klein, Jean-Claude Saut, Nikola Stoilov

We present a detailed numerical study of the stability under periodic perturbations of line solitons of two-dimensional, generalized Zakharov-Kuznetsov equations with various power nonlinearities. In the $L^{2}$-subcritical case, in accordance with a

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::490322a30a790584c9accdf2b6ec89a7
http://arxiv.org/abs/2204.11646

Numerical study of break-up in solutions to the dispersionless Kadomtsev–Petviashvili equation

Autor: Christian Klein, Nikola Stoilov

Publikováno v: Letters in Mathematical Physics
Letters in Mathematical Physics, Springer Verlag, 2021, 111 (5), ⟨10.1007/s11005-021-01454-6⟩

We present a numerical approach to study solutions to the dispersionless Kadomtsev–Petviashvili (dKP) equation on $${\mathbb {R}}\times {\mathbb {T}}$$ . The dependence on the coordinate x is considered on the compactified real line, and the depend

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d661f8df2bdc4a58fa02971d951f31fd
https://doi.org/10.1007/s11005-021-01454-6

Multi-domain spectral approach with Sommerfeld condition for the Maxwell equations

Autor: Christian Klein, Nikola Stoilov

Publikováno v: Journal of Computational Physics
Journal of Computational Physics, Elsevier, 2021, 434, pp.110149. ⟨10.1016/j.jcp.2021.110149⟩

We present a multidomain spectral approach with an exterior compactified domain for the Maxwell equations for monochromatic fields. The Sommerfeld radiation condition is imposed exactly at infinity being a finite point on the numerical grid. As an ex

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::dafc2d091341da10cb517e6d1920d91d
https://hal.archives-ouvertes.fr/hal-03283204

Numerical Study of Zakharov–Kuznetsov Equations in Two Dimensions

Autor: Nikola Stoilov, Christian Klein, Svetlana Roudenko

Publikováno v: Journal of Nonlinear Science
Journal of Nonlinear Science, Springer Verlag, 2021, 31 (2), pp.36. ⟨10.1007/s00332-021-09680-x⟩

We present a detailed numerical study of solutions to the (generalized) Zakharov–Kuznetsov equation in two spatial dimensions with various power nonlinearities. In the $$L^{2}$$ -subcritical case, numerical evidence is presented for the stability o

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ede7b16d72bd8ed1f9aba81bd92afc77
https://hal.archives-ouvertes.fr/hal-03303398

High precision numerical approach for Davey–Stewartson II type equations for Schwartz class initial data

Autor: Kenneth D.T-R McLaughlin, Christian Klein, Nikola Stoilov

Publikováno v: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Royal Society, The, 2020, 476 (2239), pp.20190864. ⟨10.1098/rspa.2019.0864⟩

We present an efficient high-precision numerical approach for Davey–Stewartson (DS) II type equa- tions, treating initial data from the Schwartz class of smooth, rapidly decreasing functions. As with previous approaches, the presented code uses dis

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::67afec17d7e50322df9fb44090a0919d
https://doi.org/10.1098/rspa.2019.0864