50 citations · 59 across the 23 of their papers we have counts for
8 papers · 1 filter
Bright and dark breathers on an elliptic wave in the defocusing mKdV equation
Dmitry E. Pelinovsky, Rudi Weikard
Breathers on an elliptic wave background consist of nonlinear superpositions of a soliton and a periodic wave, both traveling with different wave speeds and interacting periodicall…
Selection of the ground state on a compact metric graph
Robert Marangell, Dmitry E. Pelinovsky
We show that the ground state in the Fisher--KPP model on a compact metric graph with Dirichlet conditions on boundary vertices is either trivial (zero) or nontrivial and strictly…
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…
Kink breathers on a traveling wave background in the defocusing modified Korteweg--de Vries equation
Lynnyngs Kelly Arruda, Dmitry E. Pelinovsky
We characterize a general traveling periodic wave of the defocusing mKdV (modified Korteweg--de Vries) equation by using a quotient of products of Jacobi's elliptic theta functions…
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…