# Variational approach for the quantum Zakharov system

## Abstract

The quantum Zakharov system is described in terms of a Lagrangian formalism. A time-dependent Gaussian trial function approach for the envelope electric field and the low-frequency part of the density fluctuation leads to a coupled, nonlinear system of ordinary differential equations. In the semiclassical case, linear stability analysis of this dynamical system shows a destabilizing role played by quantum effects. Arbitrary values of the quantum effects are also considered, yielding the ultimate destruction of the localized, Gaussian trial solution. Numerical simulations are shown for both the semiclassical and the full quantum cases.

- Authors:

- Universidade do Vale do Rio dos Sinos, Unidade de Exatas e Tecnologicas, Av. Unisinos, 950, 93022-000 Sao Leopoldo, RS (Brazil)

- Publication Date:

- OSTI Identifier:
- 20974929

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physics of Plasmas; Journal Volume: 14; Journal Issue: 4; Other Information: DOI: 10.1063/1.2722271; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; DIFFERENTIAL EQUATIONS; ELECTRIC FIELDS; FLUCTUATIONS; LAGRANGIAN FUNCTION; MATHEMATICAL SOLUTIONS; NONLINEAR PROBLEMS; PLASMA; PLASMA DENSITY; PLASMA INSTABILITY; PLASMA SIMULATION; SEMICLASSICAL APPROXIMATION; SOLITONS; TIME DEPENDENCE; VARIATIONAL METHODS

### Citation Formats

```
Haas, F.
```*Variational approach for the quantum Zakharov system*. United States: N. p., 2007.
Web. doi:10.1063/1.2722271.

```
Haas, F.
```*Variational approach for the quantum Zakharov system*. United States. doi:10.1063/1.2722271.

```
Haas, F. Sun .
"Variational approach for the quantum Zakharov system". United States.
doi:10.1063/1.2722271.
```

```
@article{osti_20974929,
```

title = {Variational approach for the quantum Zakharov system},

author = {Haas, F.},

abstractNote = {The quantum Zakharov system is described in terms of a Lagrangian formalism. A time-dependent Gaussian trial function approach for the envelope electric field and the low-frequency part of the density fluctuation leads to a coupled, nonlinear system of ordinary differential equations. In the semiclassical case, linear stability analysis of this dynamical system shows a destabilizing role played by quantum effects. Arbitrary values of the quantum effects are also considered, yielding the ultimate destruction of the localized, Gaussian trial solution. Numerical simulations are shown for both the semiclassical and the full quantum cases.},

doi = {10.1063/1.2722271},

journal = {Physics of Plasmas},

number = 4,

volume = 14,

place = {United States},

year = {Sun Apr 15 00:00:00 EDT 2007},

month = {Sun Apr 15 00:00:00 EDT 2007}

}

DOI: 10.1063/1.2722271

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