Similarity solutions for converging shocks in a relaxing gas

Asymptotical Solutions for a Vibrationally Relaxing Gas

“…The system of equations obtained in equation (3.10) is (mathematically) the same system obtained in [24] and [16], for the compressible Euler equations of gas dynamics. The thing that changes is the physical meaning of the various parameters (coupling kernel K in the integral term, wave velocities, etc.)…”

“…There has been widespread interest in the nonlinear wave phenomena. The work of Whitham [28], Moodie et al [18], He and Moodie ([9,10]), Shtaras [27], Kalyakin [13], Krylovas and Čiegis ( [14,15]), Sharma and Radha [24], Sharma and Srinivasan [25], Sharma and Arora [23], Arora and Sharma [3], and Arora ( [1,2]) is worth mentioning in the context of nonlinear wave propagation in gas dynamic media.…”

Solutions of Inviscid Burgers’ and Equal Width Wave Equations by RDTM

“…A broad class of analytical solution methods and numerical solution methods were applied to solve these partial differential equations by Morrison et al [1], Gardner and Gardner [2], Smith [3], Courant and Friedrichs [4], Evans and Bulut [5], Wazwaz ([6] and [7]), He ([8] and [9]), Keskin [10], Peregrine [11], Bluman and Kumei [12], Whitham [13], Hunter and Keller [14], He and Moodie [15], Sharma and Radha [16], Sharma and Srinivasan [17] and Arora and Sharma [18] etc.wave equation.…”

“…Then the differential inverse transformation of the set of values gives approximation solution as (16) where n is the order of approximation solution. Hence the exact solution of the problem is given by (17) B.…”

Lie-group theoretic method for analyzing interaction of discontinuous waves in a relaxing gas

“…By an expanded Lie Group of transformations of partial differential equations we mean a continuous group of transformations acting on the expanded space of variables which includes the equation parameters in addition to independent and dependent variables. Radha & Sharma [1] exploited the Lie Group Method described in Bluman Cole [2], Bluman Kumei [3] and Logan & Perez [4] to establish the entire class of self-similar solutions for converging shocks in a relaxing gas. The method enables to characterize the medium for which the problem is invariant and admits self-similar solutions.…”