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On full Zakharov equation and its approximations

BOBKOV, V., DRÁBEK, P., ILYASOV, Y. On full Zakharov equation and its approximations. PHYSICA D-NONLINEAR PHENOMENA, 2020, roč. 401, č. January 2020, article 132168, s. 1-8. ISSN: 0167-2789
Jazyk publikace: eng
Anglický název: On full Zakharov equation and its approximations
Rok vydání: 2020
Autoři: Vladimír Bobkov , prof. RNDr. Pavel Drábek DrSc. , prof. Yavdat Ilyasov DrSc.
Abstrakt EN: We study the solvability of the Zakharov equation in a bounded domain under homogeneous Dirichlet or Navier boundary conditions. This problem is a consequence of the system of equations derived by Zakharov to model the Langmuir collapse in plasma physics. Assumptions for the existence and nonexistence of a ground state solution as well as the multiplicity of solutions are discussed. Moreover, we consider formal approximations of the Zakharov equation obtained by the Taylor expansion of the exponential term. We illustrate that the existence and nonexistence results are substantially different from the corresponding results for the original problem.
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