2007/10/16 by Nataliya M. Ivanova, N. M. Ivanova, Roman O. Popovych +5 · 2 citations
Mathematics · Physics and Astronomy · #Differential Equations and Numerical Methods #Nonlinear Waves and Solitons #Numerical methods for differential equations #math-ph #math.MP #msc:35A30 #msc:35K05 #msc:35K57
paper · pdf · doi:10.48550/arxiv.0710.3049
19 pages
arxiv created 2007/10/16 · arxiv updated 2009/12/01
This is the second part of the series of papers on symmetry properties of a class of variable coefficient (1+1)-dimensional nonlinear diffusion-convection equations of general form f(x)ut=(g(x)A(u)ux)x+h(x)B(u)ux. At first, we review the results of Part 1 of the series on equivalence transformations and group classification of the class under consideration. Investigation of non-trivial limits of parameterized subclasses of equations from the given class, which generate contractions of the corresponding maximal Lie invariance algebras, leads to the natural notion of contractions of systems of differential equations. After a brief discussion on contractions of symmetries, equations and solutions in general case, such types of contractions are studied for diffusion--convection equations. A detailed symmetry analysis of an interesting equation from the class under consideration is performed. Exact solutions of some subclasses of the considered class are also given.