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On weakly nonlinear waves in media exhibiting mixed nonlinearity

DSpace at IIT Bombay

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Title On weakly nonlinear waves in media exhibiting mixed nonlinearity
 
Creator SRINIVASAN, GK
SHARMA, VD
 
Subject hyperbolic waves
equations
hyperbolic systems
conservation laws
geometrical optics
mixed nonlinearities
 
Description We obtain the transport equations governing small amplitude high frequency disturbances, that include both quadratic and cubic nonlinearities inherent in hyperbolic systems of conservation laws. The coefficients of the nonlinear terms in the transport equation are obtained in terms of the Glimm interaction coefficients. For symmetric and isotropic systems the mean curvature of the wave front, which appears as the coefficient of the linear term in the transport equation, is shown to be related to the derivative of the ray tube area along the bicharacteristics; the amplitude of the disturbance is shown to become unbounded in the neighborhood of the point where the ray tube collapses. We also obtain a formula, akin to the one obtained by R. Rosales (1991), for the energy dissipated across shocks. (C) 2003
 
Publisher ACADEMIC PRESS INC ELSEVIER SCIENCE
 
Date 2011-07-12T16:35:05Z
2011-12-26T12:48:58Z
2011-12-27T05:34:32Z
2011-07-12T16:35:05Z
2011-12-26T12:48:58Z
2011-12-27T05:34:32Z
2003
 
Type Article
 
Identifier JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 285(2), 629-641
0022-247X
http://dx.doi.org/10.1016/S0022-247X(03)00452-9
http://dspace.library.iitb.ac.in/xmlui/handle/10054/3382
http://hdl.handle.net/10054/3382
 
Language en