# On full Zakharov equation and its approximations

@article{Bobkov2019OnFZ, title={On full Zakharov equation and its approximations}, author={Vladimir Bobkov and Pavel Dr'abek and Yavdat Ilyasov}, journal={Physica D: Nonlinear Phenomena}, year={2019}, volume={401}, pages={132168} }

Abstract We study the solvability of the Zakharov equation Δ 2 u + ( κ − ω 2 ) Δ u − κ div e − | ∇ u | 2 ∇ u = 0 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…

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