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Invariant differential equations and the Adler–Gel’fand–Dikii bracket
In this paper we find an explicit formula for the most general vector evolution of curves on RPn−1 invariant under the projective action of SL(n,R). When this formula is applied to theExpand
Symmetries of the discrete Burgers equation
A discrete Cole-Hopf transformation is used to derive a discrete Burgers equation that is linearizable to a discrete heat equation. A five-dimensional symmetry algebra is obtained that reduces to theExpand
Classification of invariant wave equations
In this paper we characterize the possible symmetry groups of wave equations and certain evolutionary generalizations, in a single time variable and one or more spatial variables. Furthermore, weExpand
Geometric Integrability of the Camassa-Holm Equation. II
It is known that the Camassa–Holm (CH) equation describes pseudo-spherical surfaces and that therefore its integrability properties can be studied by geometrical means. In particular, the CH equationExpand
Toward the classification of third-order integrable evolution equations
A non-standard way of representing an evolution equation in the form of a system is proposed. This representation allows us to investigate all the different classes of third-order integrableExpand
Integrable Quasilinear Equations
We develop a classification scheme for integrable third-order scalar evolution equations using the symmetry approach to integrability. We use this scheme to study quasilinear equations of aExpand
Compacton equations and integrability: The rosenau-hyman and Cooper-Shepard-Sodano equations
We study integrability --in the sense of admitting recursion operators-- of two nonlinear equations which are known to possess compacton solutions: the $K(m,n)$ equation introduced by Rosenau andExpand
Nonlinear gyrotropic vortex dynamics in ferromagnetic dots
The quasistationary and transient (nanosecond) regimes of nonlinear vortex dynamics in a soft magnetic dot driven by an oscillating external field are studied. We derive a nonlinear dynamical systemExpand
We review the theory of nonlocal symmetries of nonlinear partial differential equations and, as examples, we present infinite-dimensional Lie algebras of nonlocal symmetries of the Fokas–Qiao andExpand
Lie algebra contractions and symmetries of the Toda hierarchy
The Lie algebra L(Δ) of generalized and point symmetries of the equations in the Toda hierarchy is shown to be a semidirect sum of two infinite-dimensional Lie algebras, one perfect, the otherExpand