50 citations · 330 across the 31 of their papers we have counts for
5 papers · 1 filter
The stochastic integrable AKNS hierarchy
Alexis Arnaudon
We derive a stochastic AKNS hierarchy using geometrical methods. The integrability is shown via a stochastic zero curvature relation associated with a stochastic isospectral proble…
Un-reduction in field theory, with applications
Alexis Arnaudon, Marco Castrillon Lopez, Darryl D. Holm
The un-reduction procedure introduced previously in the context of Mechanics is extended to covariant Field Theory. The new covariant un-reduction procedure is applied to the probl…
Covariant un-reduction for curve matching
Alexis Arnaudon, Marco Castrillon Lopez, Darryl D. Holm
The process of un-reduction, a sort of reversal of reduction by the Lie group symmetries of a variational problem, is explored in the setting of field theories. This process is app…
On a deformation of the nonlinear Schrödinger equation
Alexis Arnaudon
We study a deformation of the nonlinear Schrödinger equation recently derived in the context of deformation of hierarchies of integrable systems. This systematic method also led to…
On a Lagrangian reduction and a deformation of completely integrable systems
Alexis Arnaudon
We develop a theory of Lagrangian reduction on loop groups for completely integrable systems after having exchanged the role of the space and time variables in the multi-time inter…