Breathers or oscillating wave packets, along with solitons, are the most energy-carrying
waves in various physical media, ie surface and internal waves, optical networks, and …

The soliton resolution for the focusing modified Korteweg-de Vries (mKdV) equation is
established for initial conditions in some weighted Sobolev spaces. Our approach is based …

In this note, we show that for a large class of nonlinear wave equations with odd
nonlinearities, any globally defined odd solution which is small in the energy space decays …

In this note, we review stability properties in energy spaces of three important nonlinear
Schrödinger breathers: Peregrine, Kuznetsov-Ma, and Akhmediev. More precisely, we show …

This paper sheds new light on the stability properties of solitary wave solutions associated
with Korteweg–de Vries-type models when the dispersion is very low. Using a compact …

The initial-boundary value problem (ibvp) for a coupled system of modified Korteweg-de
Vries (mKdV) equations depending on a parameter α is studied on the half-line. It is shown …

In this paper our first aim is to identify a large class of non-linear functions f (·) for which the
IVP for the generalized Korteweg–de Vries equation does not have breathers or “small” …

In this paper we describe stability properties of the Sine-Gordon breather solution. These
properties are first described by suitable variational elliptic equations, which also implies …

We consider the sine-Gordon (SG) equation in 1+ 1 dimensions. The kink is a static, non
symmetric exact solution to SG, stable in the energy space H 1× L 2. It is well-known that the …

We study the periodic modified KdV equation, where a periodic in space and time breather
solution is known from the work of Kevrekidis et al.[19]. We show that these breathers satisfy …