Pseudo-potentials, nonlocal symmetries and integrability of some shallow water equations
✍ Scribed by Enrique G. Reyes
- Publisher
- SP Birkhäuser Verlag Basel
- Year
- 2006
- Tongue
- English
- Weight
- 300 KB
- Volume
- 12
- Category
- Article
- ISSN
- 1022-1824
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## Abstract The complete symmetry group of a 1 + 1 evolution equation has been demonstrated to be represented by the six‐dimensional Lie algebra of point symmetries __sl__(2, __R__) ⊕~__s__~__W__, where __W__ is the three‐dimensional Heisenberg–Weyl algebra. We construct a complete symmetry group o
The local symmetries and conservation laws are calculated for the equations of shallow water with an axisymmetric profile of bottom under the assumption that the corresponding generating functions may depend only on all variables and their derivatives up to the second order. It is shown that if the
The concept of the complete symmetry group of a differential equation introduced by J. Krause (1994, J. Math. Phys. 35, 5734-5748) is extended to integrals of such equations. This paper is devoted to some aspects characterising complete symmetry groups. The algebras of the symmetries of both differe