4 papers · 1 filter
On the ground state of the nonlinear Schr{ö}dinger equation: asymptotic behavior at the endpoint powers
Rémi Carles, Quentin Chauleur, Guillaume Ferriere +1
We consider the ground states of the nonlinear Schr{ö}dinger equation, which stand for radially symmetric and exponentially decaying solutions on the full space. We investigate th…
Orbital stability of kinks in the NLS equation with competing nonlinearities
Justin Holmer, Panayotis G. Kevrekidis, Dmitry E. Pelinovsky
Kinks connecting zero and nonzero equilibria in the NLS equation with competing nonlinearities occur at the special values of the frequency parameter. Since they are minimizers of…
On smooth and peaked traveling waves in a local model for shallow water waves
Spencer Locke, Dmitry E. Pelinovsky
We introduce a new model equation for Stokes gravity waves based on conformal transformations of Euler's equations. The local version of the model equation is relevant for dynamics…
Peaked Stokes waves as solutions of Babenko's equation
Spencer Locke, Dmitry E. Pelinovsky
Babenko's equation describes traveling water waves in holomorphic coordinates. It has been used in the past to obtain properties of Stokes waves with smooth profiles analytically a…