Approximate Symmetries of the Harry Dym Equation

We derive the first-order approximate symmetries for the Harry Dym equation by the method of approximate transformation groups proposed by Baikov et al. (1989, 1996). Moreover, we investigate the structure of the Lie algebra of symmetries of the perturbed Harry Dym equation. We compute the one-dimensional optimal system of subalgebras as well as point out some approximately differential invariants with respect to the generators of Lie algebra and optimal system.

SYMMETRY ANALYSIS AND SIMILARITY REDUCTION OF THE KORTEWEG–DE VRIES–ZAKHAROV–KUZNETSOV EQUATION

In this paper, the problem of determining the largest possible set of symmetries for an important nonlinear dynamical system in mathematical physics, the Korteweg–de Vries–Zakharov–Kuznetsov (KdV–ZK) equation, is studied. By applying the basic Lie symmetry method for the KdV–ZK equation, the classical Lie point symmetry operators are obtained. Also, the structure of the Lie algebra of symmetries is discussed and the optimal system of subalgebras of the equation is constructed. The Lie invariants as well as similarity reduced equations corresponding to infinitesimal symmetries are obtained. The non-classical symmetries of the KdV–ZK equation are also investigated.

OPTIMAL SYSTEMS AND GROUP INVARIANT SOLUTIONS FOR A MODEL ARISING IN FINANCIAL MATHEMATICS

We consider a bond‐pricing model described in terms of partial differential equations (PDEs). Classical Lie point symmetry analysis of the considered PDEs resulted in a number of point symmetries being admitted. The one‐dimensional optimal system of subalgebras is constructed. Following the symmetry reductions, we determine the group‐invariant solutions.