Eigenvalues of kinematical conservation laws (KCL) based 3-D weakly nonlinear ray theory (WNLRT)

Arun, K. R. ; Prasad, Phoolan (2010) Eigenvalues of kinematical conservation laws (KCL) based 3-D weakly nonlinear ray theory (WNLRT) Applied Mathematics and Computation, 217 (5). pp. 2285-2288. ISSN 0096-3003

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Official URL: http://linkinghub.elsevier.com/retrieve/pii/S00963...

Related URL: http://dx.doi.org/10.1016/j.amc.2010.06.041


System of kinematical conservation laws (KCL) govern evolution of a curve in a plane or a surface in space, even if the curve or the surface has singularities on it. In our recent publication [K.R. Arun, P. Prasad, 3-D kinematical conservation laws (KCL): evolution of a surface in R3-in particular propagation of a nonlinear wavefront, Wave Motion 46 (2009) 293–311] we have developed a mathematical theory to study the successive positions and geometry of a 3-D weakly nonlinear wavefront by adding an energy transport equation to KCL. The 7 × 7 system of equations of this KCL based 3-D weakly nonlinear ray theory (WNLRT) is quite complex and explicit expressions for its two nonzero eigenvalues could not be obtained before. In this short note, we use two different methods: (i) the equivalence of KCL and ray equations and (ii) the transformation of surface coordinates, to derive the same exact expressions for these eigenvalues. The explicit expressions for nonzero eigenvalues are important also for checking stability of any numerical scheme to solve 3-D WNLRT.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Kinematical Conservation Laws; Ray Theory; Nonlinear Wave; Polytropic Gas; Weakly Hyperbolic System
ID Code:37667
Deposited On:25 Apr 2011 10:20
Last Modified:17 May 2016 20:33

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