Search

We provide a complete classification of point symmetries and low-order local conservation laws of the generalized quasilinear KdV equation in terms of the arbitrary function. The corresponding interpretation of symmetry transformation groups are given. In addition, a physical description of the conserved quantities is included. Finally, few travelling wave solutions have been obtained. [ABSTRACT FROM AUTHOR]

In this paper, we consider a generalized variable-coeficient Gardner equation. By using the equivalence group of this equation, we derive the differential invariants of first order and the corresponding invariant equations. We employ these differential invariants and invariant equations to find the most general subclass of variable-coeficient Gardner equations which can be mapped into a specific constant-coeficient equation by means of an equivalence transformation. Furthermore, differential invariants are applied to obtain exact solutions. [ABSTRACT FROM AUTHOR]

In the present work we make an analysis of the Korteweg-de Vries of sixth order. We apply the classical Lie method of infinitesimals and the nonclassical method, due to Bluman and Cole, to deduce new symmetries of the equation which cannot be obtained by Lie classical method. Moreover, we obtain ten different conservation laws depending on the parameters and we conclude that potential symmetries project on the infinitesimals corresponding to the classical symmetries. [ABSTRACT FROM AUTHOR]