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Modulated deep-water 1D Stokes waves are considered experimentally and theoretically. Wave trains are modulated in a controlled fashion and their evolution is recorded. Data from repeated laboratory experiments are reproducible near the wave maker, but diverge away from the wave maker. Numerical integration of a perturbed nonlinear Schrödinger equation and… (More)

- Alvaro L. Islas, Constance M. Schober
- Future Generation Comp. Syst.
- 2003

- Alvaro L. Islas, Constance M. Schober
- Mathematics and Computers in Simulation
- 2005

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)

- Constance M. Schober, Tomasz H. Wlodarczyk
- J. Comput. Physics
- 2008

- Håvard Berland, Alvaro L. Islas, Constance M. Schober
- J. Comput. Physics
- 2007

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)

- M. Hederi, Alvaro L. Islas, K. Reger, Constance M. Schober
- Mathematics and Computers in Simulation
- 2016

- Alvaro L. Islas, Constance M. Schober
- Future Generation Comp. Syst.
- 2006

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)

- Brian E. Moore, Laura Noreña, Constance M. Schober
- J. Comput. Physics
- 2013

- Constance M. Schober, Tomasz H. Wlodarczyk
- Mathematics and Computers in Simulation
- 2009

Homoclinic varieties play a crucial role in the dynamics of perturbations of the focusing Nonlinear Schrr odinger equation (NLS). We undertake a Mel'nikov analysis to investigate the possibility of persistence of transversal homoclinic orbits for a conservative perturbation of the NLS.