Article ID Journal Published Year Pages File Type
1901038 Reports on Mathematical Physics 2013 13 Pages PDF
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.

Related Topics
Physical Sciences and Engineering Mathematics Mathematical Physics
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