arXiv subjects
Publications and source records attributed to S. Dimas.
The enhanced group classification of a semi-linear generalization of a general bond-pricing equation is carried out by employing the underlying equivalence and additional equivalence transformations. The knowledge of the sub classes with larger Lie algebras than the general case enable us to find non trivial invariant solutions under the terminal and the barrier option condition.
The complete group classification of a generalization of the Heath model is carried out by connecting it to the heat equation with nonlinear source. Examples of invariant solutions are given under the terminal and the barrier option condition.
The two-dimensional anisotropic Kuramoto-Sivashinsky equation is a forth-order nonlinear evolution equation in two spatial dimensions that arises in sputter erosion and epitaxial growth on vicinal surfaces. A generalization of this equation is proposed and studied via group analysis methods. The complete group classification of this generalized Kuramoto-Sivashinsky equation is carried out, it is classified according to the property of the self-adjointness and the corresponding conservation laws are established.