2014 1(14)

Back to table of content

   Short abstract

 

Pages:

55 - 59

Language:

RU

Ref.:

6


Click to get extended abstract


Download paper: [RU]

2014_1(14)_9.pdf

 

 

INTEGRIABILITY OF MULTY RESONANCE LORENZ MEDIA WITH QUADRATIC NONLINEARITY BY IST METHOD

Gasenko V.G.

Institute of Thermophysics SB RAS, Novosibirsk, Russia


Citation:

Gasenko, V.G., (2014) Integriability of multy resonance Lorenz media with quadratic nonlinearity by IST method, Modern Science: Researches, Ideas, Results, Technologies, Iss. #1(14), PP. 55 - 59.


Keywords:

multiresonant Lorentz environment; IST method; the wave equation


Abstracts:

High order nonlinear wave equation for the polydispersive gas-liquid mixture with a few bubble’s sizes as a sample of Lorenz media with quadratic nonlinearity was yielded. This equation named Multy Resonace KdV (MrKdV) equation easy transform to KdV equation in a case of long one side propagating waves as far as to NLS equation for the case of envelope waves and cubic nonlinearity. The full integriability of MrKdV in two resonance case by IST method was shown: Lax pair and the form of unscattering potentials was found. The purpose of this work is theoretical investigation of nonlinear waves in Lorenz medias with quadratic nonlinearity as in bubbled liquids with two bubble’s sizes. The analysis methods was numerical and Inverse Scattering Transform (IST) analytical method. The main result of presented paper is successful use of IST method for analysis of nonlinear waves in polydispersive gas-liquid mixture as a form of two resonance Lorenz media.


References:

  1. Nakoryakov, V.E. and Pokusaev, B.G. and Shreyber, I.R. (1990). Volnovaya dinamika gaso I parozhidkostnykh sred [Wave dynamics of gas-liquid mixtures], Energoatomizdat, Moskow, USSR.

  2. Gasenko V.G., Dontsov V.E., Nakoryakov B.E. (2002). On the structure of complicated shape solitary waves in a liquid with gas bubbles due to two different bubbles' sizes // Proceedings of 2-nd Biot conference on Poromechanics, Grenoble-France, August 26-28, 2002, pp.715-721.

  3. V.G. Gasenko and V.E. Nakoryakov.J. Eng. Thermophysics 17, 158 (2007).

  4. Petviashvili, V.I. (1976). "About unusual soliton equation", Fizika plazmy, Vol.2, no.3, pp.469-472.

  5. Miura R.M., Gardner C.S., Kruskal M.D. Korteweg-de Vries equation and generalizations. II. Existence of conservation laws and constants of motion // J. Math. Phys. 1968. Vol. 9, № 8. P. 1204-1209.

  6. Захаров В.Е., Шабат А.Б. Точная теория двумерной самофокусировки и одномерной автомодуляции волн в нелинейных средах // ЖЭТФ. 1971. Т. 61, № 1. С. 118-134.

 

 
     

© SPIC "Kappa", LLC 2009-2016