229 citations · 1.3k across the 55 of their papers we have counts for
55 papers
Exact periodic solutions of the generalized Constantin-Lax-Majda equation with dissipation
Denis A. Silantyev, Pavel M. Lushnikov, Michael Siegel +1
We present exact pole dynamics solutions to the generalized Constantin-Lax-Majda (gCLM) equation in a periodic geometry with dissipation , where its spatial Fourier transform…
The instability of near-extreme Stokes waves
Bernard Deconinck, Sergey A. Dyachenko, Pavel M. Lushnikov +1
We study the stability of Stokes waves on a free surface of an ideal fluid of infinite depth. For small steepness the modulational instability dominates the dynamics, but its growt…
Global existence and singularity formation for the generalized Constantin-Lax-Majda equation with dissipation: The real line vs. periodic domains
David M. Ambrose, Pavel M. Lushnikov, Michael Siegel +1
The question of global existence versus finite-time singularity formation is considered for the generalized Constantin-Lax-Majda equation with dissipation , where $\widehat {…
Superharmonic Instability of Stokes Waves
Alexander O. Korotkevich, Pavel M. Lushnikov, Anastassiya A. Semenova +1
A stability of nearly limiting Stokes waves to superharmonic perturbations is considered numerically. The new, previously inaccessible branches of superharmonic instability were in…
Collapse vs. blow up and global existence in the generalized Constantin-Lax-Majda equation
Pavel M. Lushnikov, Denis A. Silantyev, Michael Siegel
The question of finite time singularity formation vs. global existence for solutions to the generalized Constantin-Lax-Majda equation is studied, with particular emphasis on the in…
Comparison of Split-Step and Hamiltonian Integration Methods for Simulation of the Nonlinear Schrödinger Equation
Anastassiya Semenova, Sergey A. Dyachenko, Alexander O. Korotkevich +1
We provide a systematic comparison of two numerical methods to solve the widely used nonlinear Schrödinger equation. The first one is the standard second order split-step (SS2) met…