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Invariant differential equations and the Adler–Gel’fand–Dikii bracket

- A. González-López, R. H. Heredero, +6 authors Wi
- Mathematics, Physics
- 29 March 1996

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 the… Expand

Symmetries of the discrete Burgers equation

- R. H. Heredero, D. Levi, P. Winternitz
- Mathematics
- 9 April 1999

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 the… Expand

Classification of invariant wave equations

- R. H. Heredero, P. Olver
- Mathematics
- 1 December 1996

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, we… Expand

Geometric Integrability of the Camassa-Holm Equation. II

- R. H. Heredero, E. Reyes
- Mathematics
- 1 July 2011

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 equation… Expand

Toward the classification of third-order integrable evolution equations

- R. H. Heredero, V. Sokolov, S. I. Svinolupov
- Mathematics
- 7 July 1994

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 integrable… Expand

Integrable Quasilinear Equations

- R. H. Heredero
- Mathematics
- 1 November 2002

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 a… Expand

Compacton equations and integrability: The rosenau-hyman and Cooper-Shepard-Sodano equations

- R. H. Heredero, M. Euler, N. Euler, E. Reyes
- Physics
- 2 April 2019

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 and… Expand

Nonlinear gyrotropic vortex dynamics in ferromagnetic dots

- K. Guslienko, R. H. Heredero, O. Chubykalo-Fesenko
- Physics
- 8 July 2010

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 system… Expand

NONLOCAL SYMMETRIES, COMPACTON EQUATIONS, AND INTEGRABILITY

- R. H. Heredero, E. Reyes
- Mathematics
- 30 August 2013

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 and… Expand

Lie algebra contractions and symmetries of the Toda hierarchy

- R. H. Heredero, D. Levi, M. Rodŕıguez, P. Winternitz
- Mathematics
- 21 July 2000

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 other… Expand

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