Organizers of this minisymposium are
Long wave approximations of dispersive wave problems such as the water wave problem go at least back to the 19th century. Famous equations auch as the Korteweg-de Vries (KdV) equation or Whitham’s modulation equations (WMEs), have been derived by perturbation analysis for an approximate description of the underlying wave phenomena. Error estimates for long wave approximations have been established since the 1980s.
The last years have seen various new developments about long wave approximations in homogeneous, periodic and stochastic media. This minisymposium aims to address the recent results and trends in the following topics
- Use of WMEs in dissipative systems, in particular in the stability analysis of periodic solutions
- Validity proofs for WMEs in Gevrey and Sobolev spaces for nonlinear Schrödinger equations
- Validity of WMEs in case of additional resonances
- Long wave approximations in stochastic Fermi-Pasta-Ulam systems
- Validity of the KdV approximation for nonlinear wave equations on quantum graphs
- Hamiltonian studies on counter-propagating waves
- Convergence of mechanical balance laws