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math.AP2014
Variants of the focusing NLS equation. Derivation, justification and open problems related to filamentation
Eric Dumas, David Lannes, Jeremie Szeftel
The focusing cubic NLS is a canonical model for the propagation of laser beams. In dimensions 2 and 3, it is known that a large class of initial data leads to finite time blow-up.…
math.AP2014
Justification of the log-KdV equation in granular chains: the case of precompression
Eric Dumas, Dmitry Pelinovsky
For travelling waves with nonzero boundary conditions, we justify the logarithmic Korteweg-de Vries equation as the leading approximation of the Fermi-Pasta-Ulam lattice with Hertz…