Rudolf Schmid

TL;DR: In this paper, a class of symplectic integration schemes to general Sine-Gordon type systems is presented. Butler et al. also conduct several numerical tests for these symplectic schemes and demonstrate the effectiveness of these schemes for numerical computation of the solutions to the SING types.

TL;DR: In this article, the authors generalized finite-dimensional Hamiltonian systems to infinite-dimensional systems and applied them to construct finite difference schemes for the nonlinear wave equation and showed that these schemes compare favorably with conventional difference methods.

TL;DR: In this article, the authors define the BRST bicomplex in terms of local cohomology using differential forms on the infinite jet bundle and consider variational aspects of the problem in this cohomological context.

TL;DR: In this article, it has been shown that the solutions of competitive and cooperative systems have limit sets which cannot be more complicated than invariant sets of systems of one lower dimension, in particular, autonomous 2-dimensional systems of these types have only "trivial" dynamics in the sense that all bounded solutions approach equilibrium asymptotically.