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The Quarterly Journal of Mechanics and Applied Mathematics 1991 44(2):323-331; doi:10.1093/qjmam/44.2.323
© 1991 by Oxford University Press
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A METHOD OF OBTAINING EXACT PARTICULAR SOLUTIONS OF A SYSTEM OF TWO FIRST-ORDER QUASILINEAR PARTIAL DIFFERENTIAL EQUATIONS

ANATOLY ODULO

( Applied Science Associates, Inc. 70 Dean Knauss Drive, Narragansett, Rhode Island 02882, USA )

A theorem showing the way to obtain exact particular solutions of a system of two first-order quasilinear equations is proved. The use of this theorem is demonstrated on the shallow-water equations.

In all described cases, use of the theorem leads to exact particular solutions in parametric form, obtained by solving simpler systems which are reduced to ordinary differential equations through separation of variables.


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