A variational approach to Lax representations

A Kleisli-based Approach to Lax Algebras

By exploiting the description of topological spaces by either neighborhood systems or filter convergence, we obtain a neighborhood-like presentation of categories of lax algebras. The simplicity of this presentation pinpoints the importance of the Kleisli extension, which is introduced as a particular lax extension of the associated monad functor.

More on stochastic and variational approach to the Lax-Friedrichs scheme

Strong convergence for variational inequalities and equilibrium problems and representations

We introduce an implicit method for nding a common element of the set of solutions of systems of equilibrium problems and the set of common xed points of a sequence of nonexpansive mappings and a representation of nonexpansive mappings. Then we prove the strong convergence of the proposed implicit schemes to the unique solution of a variational inequality, which is the optimality condition for ...

A variational approach to subdivision

In this paper a new class of interpolatory re nement schemes is presented which in every re nement step determine the new points by solving an optimization problem. In general, these schemes are global, i.e., every new point depends on all points of the polygon to be re ned. By choosing appropriate quadratic functionals to be minimized iteratively during re nement, very e cient schemes producin...

Symmetry, Conserved Charges, and Lax Representations of Nonlinear Field Equations: A Unified Approach

A certain non-Noetherian connection between symmetry and integrability properties of nonlinear field equations in conservation-law form is studied. It is shown that the symmetry condition alone may lead, in a rather straightforward way, to the construction of a Lax pair, a doubly infinite set of (generally nonlocal) conservation laws, and a recursion operator for symmetries. Applications includ...