UK Nonlinear News, August 2002

Workshop on Dynamical Systems Methods in Nonlinear Wave Equations

Loughborough University, July 4-5 2002

By Vassilis Rothos

Sponsored by LMS, with support from EPSRC and Department of Mathematical Sciences, Loughborough University

The workshop took place under the auspices of the Centre for Nonlinear Mathematics and Applications, Loughborough University, and was organised by V.M. Rothos and R.H.J. Grimshaw. The workshop was attended by approximately 50 participants, of whom 10 were postgraduate students.

The talks covered a wide range of topics, ranging from homoclinic bifurcations phenomena in soliton equations, stability of multi-bump pulses and wavetrains, KAM theory and Birkhoff normal forms for nonlinear PDEs, solitons and breathers in nonlinear lattices, with applications in nonlinear optics, water waves, reaction-diffusion equations and MHD. The invited plenary speakers were:

G. Iooss INLN, Sophia-Antipolis
Water-Waves as a Spatial Dynamical System
J. Engelbrecht Tallinn
Modified KdV Evolution Equations and Solitary Waves
B. Sandstede Ohio-State
Multi-hump pulses in PDEs with reflection and phase invariance
D. Pelinovsky McMaster
Semi-stability of embedded solitons in the general fifth-order KdV equation
D. Bambusi Milan
Birkhoff Normal Form for some Nonlinear PDEs
J.C. Eilbeck Heriot-Watt
Solitons and Breathers in Nonlinear lattices
T. Bridges Surrey
Instability and breakup of standing waves (spatially periodic breathers) of nonlinear wave equations
S. Turitsyn Aston
Self-similar parabolic optical solitary waves
A. Yew Ohio-State
Stability of cnoidal waves in a nonlinear Schrodinger equation with potential
E. Pelinovsky Nizhny Novgorod
Dynamics of the large-amplitude solitary waves under the action of the weak perturbations
E. Doktorov Minsk
Solitons beyond the Zakharov-Shabat Spectral Problems

The contributed speakers were:

G. Hek Amsterdam
Pulse patterns in a coupled Ginzburg-Landau equation
H. van der Ploeg Amsterdam
Stability of pulse patterns in the Gierer-Meinhardt equation
A. Ponno Milan
A relation between stochasticity thresholds in FPU models and the threshold for soliton formation in the NLS equation
C. Martel Madrid
Dispersion and diffusion effects in counterpropagating waves
M.S. Ruderman Sheffield
DNLS soliton propagation in a plasma with fluctuating density
I. Ballai Sheffield
Solitons and their instabilities in MHD waveguides
M. Stepic Belgrade
Stationary solutions of 2D discrete NLS equation and their stability
T. Dmitrieva Saratov
Solitons, complex dynamics and chaos in three-wave parametric interaction

Overall the meeting was very successful, with a larger attendance than anticipated, excellent talks and fruitful discussions.

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Last Updated: 27th July 2002.