576 citations · 1.5k across the 43 of their papers we have counts for
4 papers · 1 filter
Persistence of invariant manifolds for nonlinear PDEs
Don A. Jones, Steve Shkoller
We prove that under certain stability and smoothing properties of the semi-groups generated by the partial differential equations that we consider, manifolds left invariant by thes…
Multisymplectic geometry, covariant Hamiltonians, and water waves
Jerrold E. Marsden, Steve Shkoller
This paper concerns the development and application of the multisymplectic Lagrangian and Hamiltonian formalism for nonlinear partial differential equations. In this theory, soluti…
Multisymplectic geometry, variational integrators, and nonlinear PDEs
Jerrold E. Marsden, George W. Patrick, Steve Shkoller
This paper presents a geometric-variational approach to continuous and discrete mechanics and field theories. Using multisymplectic geometry, we show that the existence of the fund…
Geometry and curvature of diffeomorphism groups with metric and mean hydrodynamics
Steve Shkoller
Recently, Holm, Marsden, and Ratiu [1998] have derived a new model for the mean motion of an ideal fluid in Euclidean space given by the equation $\dot{V}(t) + \nabla_{U(t)} V(t) -…