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 …

We present elliptic-rogue wave solutions for integrable nonlinear soliton equations in
rational form by elliptic functions. Unlike solutions generated on the plane wave background …

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 mainly construct and analyze the multi elliptic‐localized solutions under the background
of elliptic function solutions for the focusing modified Korteweg‐de Vries (mKdV) equation …

We show that breather solutions of the Gardner equation, a natural generalization of the KdV
and mKdV equations, are H 2 (R) stable. Through a variational approach, we characterize …

In this article we prove that 2-soliton solutions of the sine-Gordon equation (SG) are orbitally
stable in the natural energy space of the problem H 1× L 2. The solutions that we study are …

We consider the focusing Nonlinear Schrödinger equation posed on the one dimensional
line, with nonzero background condition at spatial infinity, given by a homogeneous plane …

The Boussinesq abcd system is a 4-parameter set of equations posed in R t× R x, originally
derived by Bona, Chen and Saut [11],[12] as first order 2-wave approximations of the …