# The two modes extension to the Berk-Breizman equation: Delayed differential equations and asymptotic solutions

## Abstract

The integro-differential Berk-Breizman (BB) equation, describing the evolution of particle-driven wave mode is transformed into a simple delayed differential equation form {nu}{partial_derivative}a({tau})/{partial_derivative}{tau}=a({tau}) -a{sup 2}({tau}- 1) a({tau}- 2). This transformation is also applied to the two modes extension of the BB theory. The obtained solutions are presented together with the derived asymptotic analytical solutions and the numerical results.

- Authors:

- Institute of Physics, West Pomeranian University of Technology, Szczecin (Poland)

- Publication Date:

- OSTI Identifier:
- 22043475

- Resource Type:
- Journal Article

- Journal Name:
- Physics of Plasmas

- Additional Journal Information:
- Journal Volume: 18; Journal Issue: 9; Other Information: (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1070-664X

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; ANALYTICAL SOLUTION; ASYMPTOTIC SOLUTIONS; DIFFERENTIAL EQUATIONS; NUMERICAL ANALYSIS; PARTICLES; PLASMA; SIMULATION

### Citation Formats

```
Marczynski, Slawomir.
```*The two modes extension to the Berk-Breizman equation: Delayed differential equations and asymptotic solutions*. United States: N. p., 2011.
Web. doi:10.1063/1.3639135.

```
Marczynski, Slawomir.
```*The two modes extension to the Berk-Breizman equation: Delayed differential equations and asymptotic solutions*. United States. doi:10.1063/1.3639135.

```
Marczynski, Slawomir. Thu .
"The two modes extension to the Berk-Breizman equation: Delayed differential equations and asymptotic solutions". United States. doi:10.1063/1.3639135.
```

```
@article{osti_22043475,
```

title = {The two modes extension to the Berk-Breizman equation: Delayed differential equations and asymptotic solutions},

author = {Marczynski, Slawomir},

abstractNote = {The integro-differential Berk-Breizman (BB) equation, describing the evolution of particle-driven wave mode is transformed into a simple delayed differential equation form {nu}{partial_derivative}a({tau})/{partial_derivative}{tau}=a({tau}) -a{sup 2}({tau}- 1) a({tau}- 2). This transformation is also applied to the two modes extension of the BB theory. The obtained solutions are presented together with the derived asymptotic analytical solutions and the numerical results.},

doi = {10.1063/1.3639135},

journal = {Physics of Plasmas},

issn = {1070-664X},

number = 9,

volume = 18,

place = {United States},

year = {2011},

month = {9}

}

DOI: 10.1063/1.3639135

Other availability

Save to My Library

You must Sign In or Create an Account in order to save documents to your library.