

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 gasliquid 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 gasliquid mixture as a form of two resonance Lorenz media. 
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