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Several recently developed multisymplectic schemes for Hamiltonian PDEs have been shown to preserve associated local conservation laws and constraints very well in long time numerical simulations. Backward error analysis for PDEs, or the method of modified equations, is a useful technique for studying the qualitative behavior of a discretization and… (More)

preprint numerics no. 1/2006 norwegian university of science and technology trondheim, norway The cubic nonlinear Schrödinger (nls) equation with periodic boundary conditions is solvable using Inverse Spectral Theory. The " nonlinear " spectrum of the associated Lax pair reveals topological properties of the nls phase space that are difficult to assess by… (More)

Recent results on the local and global properties of multisymplectic discretizations of Hamiltonian PDEs are discussed. We consider multisymplectic (MS) schemes based on Fourier spectral approximations and show that, in addition to a MS conservation law, conservation laws related to linear symmetries of the PDE are preserved exactly. We compare spectral… (More)

- A L Islas, C M Schober
- 2004

Using the inverse spectral theory of the nonlinear Schrödinger (NLS) equation we correlate the development of rogue waves in oceanic sea states characterized by the JONSWAP spectrum with the proximity to homoclinic solutions of the NLS equation. We find in numerical simulations of the NLS equation that rogue waves develop for JONSWAP initial data that is "… (More)

We discuss physical and statistical properties of rogue wave generation in deep water from the perspective of the focusing Nonlinear Schrödinger equation and some of its higher order generalizations. Numerical investigations and analytical arguments based on the inverse spectral theory of the underlying integrable model, perturbation analysis, and… (More)

- A Calini, C M Schober
- 2007

For certain parameter regimes, the periodic focusing nonlinear Schrr odinger equation (NLS) exhibits, under perturbation, a chaotic response characterized by irregular center-wing ipping of the wave form, when even spatial symmetry is imposed. The main source of chaos can be proven to be the transversal intersection of homoclinic manifolds of perturbed… (More)