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math.AP2026
Bifurcations of solitary waves in a coupled system of long and short waves
James Hornick, Dmitry E. Pelinovsky
We consider families of solitary waves in the Korteweg--de Vries (KdV) equation coupled with the linear Schrödinger (LS) equation. This model has been used to describe interaction…
math.AP2024
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…