Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Invariance group properties and exact solutions of equations describing time-dependent free surface flows under gravity


Authors: P. L. Sachdev and Varughese Philip
Journal: Quart. Appl. Math. 43 (1986), 463-480
MSC: Primary 76B15; Secondary 35C05
DOI: https://doi.org/10.1090/qam/846158
MathSciNet review: 846158
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Abstract: Using the method of infinitesimal transformations, a 6-parameter family of exact solutions describing nonlinear sheared flows with a free surface are found. These solutions are a hybrid between the earlier self-propagating simple wave solutions of Freeman, and decaying solutions of Sachdev. Simple wave solutions are also derived via the method of infinitesimal transformations. Incomplete beta functions seem to characterize these (nonlinear) sheared flows in the absence of critical levels.


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DOI: https://doi.org/10.1090/qam/846158
Article copyright: © Copyright 1986 American Mathematical Society


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