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Analytic and Numerical Study of N‐Waves Governed by the Nonplanar Burgers Equation
Author(s) -
Sachdev P. L.,
Rao Ch. Srinivasa,
Joseph K. T.
Publication year - 1999
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/1467-9590.00122
Subject(s) - mathematics , asymptotic expansion , planar , burgers' equation , contraction (grammar) , mathematical analysis , contraction mapping , exact solutions in general relativity , mathematical physics , partial differential equation , fixed point , medicine , computer graphics (images) , computer science
In this article, evolution of N‐waves under the nonplanar Burgers equation, which takes into account geometrical expansion or contraction, is treated analytically. An exact asymptotic solution, generalizing that for the planar Burgers equation, is given for the case of expansion. An approximate treatement, using a balancing argument, gives asymptotic analytic results for both expansion and contraction. The analysis is fortified by an accurate numerical solution of the problem. This study is brought in close conjunction with the earlier work of Crighton and Scott [13] and Sachdev, Joseph and Nair [3].