50 citations · 59 across the 23 of their papers we have counts for
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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 interactions…
Stability of periodic waves in the model with intensity--dependent dispersion
Fábio Natali, Dmitry E. Pelinovsky, Shuoyang Wang
We study standing periodic waves modeled by the nonlinear Schrodinger equation with the intensity-dependent dispersion coefficient. Spatial periodic profiles are smooth if the freq…
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 perio…
Bifurcations of unstable eigenvalues for Stokes waves derived from conserved energy
Sergey Dyachenko, Dmitry E. Pelinovsky
We address Euler's equations for irrotational gravity waves in an infinitely deep fluid rewritten in conformal variables. Stokes waves are traveling waves with the smooth periodic…
Instability of the peaked traveling wave in a local model for shallow water waves
Fábio Natali, Dmitry E. Pelinovsky, Shuoyang Wang
The traveling wave with the peaked profile arises in the limit of the family of traveling waves with the smooth profiles. We study the linear and nonlinear stability of the peaked…
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…