Some exact solutions of Burgers-type equations
Author:
P. L. Sachdev
Journal:
Quart. Appl. Math. 34 (1976), 118-122
MSC:
Primary 35C05
DOI:
https://doi.org/10.1090/qam/447764
MathSciNet review:
447764
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Abstract: A class of Burgers-type equations, reducible through a generalized Hopf—Cole transformation to a linear diffusion equation, are treated by similarity methods. New exact solutions of these equations are obtained and related to the wellknown solutions of the standard Burgers equation. Physical applications of these solutions are indicated.
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E. R. Benton and G. W. Platzman, A table of solutions of one-dimensional Burgers equation, Quart. Appl. Math. 30, 195–212 (1972)
P. L. Sachdev and R. Seebass, Propagation of spherical and cylindrical N-waves, J. Fluid Mech. 58, 197–205 (1973)
L. Sirovich and T. H. Chong, Supersonic flight in a stratified sheared atmosphere, Phys. Fluids 17, 310–320 (1974)
N. N. Romanova, The vertical propagation of short acoustic waves in the real atmosphere, Izv. Atmospheric and Oceanic Physics 16, 134–145 (1970)
J. D. Murray, Perturbation effects on the decay of discontinuous solutions of non-linear first order wave equations, SIAM J. Appl. Math. 19, 273–298 (1970)
J. D. Murray, Singular perturbations of a class of non-linear hyperbolic and parabolic equations, J. Math. Phys. 47, 111–133 (1968)
E. Y. Rodin, A Riccati solution for Burgers equations, Quart. Appl. Math. 27, 541–545 (1969)
C. W. Chu, A class of reducible system of quasi-linear partial differential equations, Quart. Appl. Math. 23, 275–278 (1965)
M. J. Lighthill, Viscosity effects in sound waves of finite amplitude, in Surveys in mechanics (G. K. Batchelor and R. M. Davies, editors), Cambridge Univ. Press, Cambridge, 1956, 250–351
G. M. Murphy, Ordinary differential equations and their solutions (p. 327), D. Van Nostrand, Princeton, 1960
E. C. Titchmarsh, Eigenfunction expansions, Part 1 (§4.2, 4.12), Oxford Univ. Press, 1962
G. A. Grinberg, On the temperature or concentration fields produced inside an infinite or finite domain by moving surfaces at which the temperature or concentration are given as functions of time, PMM 33, 1021 (1969)
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Article copyright:
© Copyright 1976
American Mathematical Society
