4 papers
Approximate Peregrine Solitons in Dispersive Nonlinear Wave Equations
Guido Schneider, Nils Thorin
The purpose of this short note is to explain how the existing results on the validity of the NLS approximation can be extended from Sobolev spaces to the spaces o…
Traveling waves in periodic metric graphs via spatial dynamics
Stefan Le Coz, Dmitry E. Pelinovsky, Guido Schneider
The purpose of this work is to introduce a concept of traveling waves in the setting of periodic metric graphs. It is known that the nonlinear Schr{ö}dinger (NLS) equation on peri…
On the long-wave approximation of solitary waves in cylindrical coordinates
James Hornick, Dmitry E. Pelinovsky, Guido Schneider
We address justification and solitary wave solutions of the cylindrical KdV equation which is formally derived as a long wave approximation of radially symmetric waves in a two-dim…
On the Existence of Generalized Breathers and Transition Fronts in Time-Periodic Nonlinear Lattices
Christopher Chong, Dmitry E. Pelinovsky, Guido Schneider
We prove the existence of a class of time-localized and space-periodic breathers (called q-gap breathers) in nonlinear lattices with time-periodic coefficients. These q-gap breathe…