Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1901038 | Reports on Mathematical Physics | 2013 | 13 Pages |
Abstract
We consider the equation utt=F(u)uxx+aF′(u)ux2, where F(u) is an arbitrary function and a ≠ 0 is a constant. The problem in question is for which functions F(u ) this equation admits the ansatz t = w1(x)d(u) + w2(x)t = w1(x)d(u) + w2(x)reducing it to a system of two ordinary differential equations with unknown functions w1(x) and w2(x). New classes of exact solutions with generalized separation of variables were constructed for these equations, which cannot be obtained by the method of classical group analysis.
Keywords
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Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
Anatoliy F. Barannyk, Tatjana A. Barannyk, Ivan I. Yuryk,