Breather solutions of the modified Korteweg-de Vries equation are shown to be globally
stable in a natural H 2 topology. Our proof introduces a new Lyapunov functional, at the H 2 …

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 study the long-time dynamics of complex-valued modified Korteweg–de Vries (mKdV)
solitons, which are distinguished because they blow up in finite time. We establish stability …

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 …

Abstract Using the Inverse Scattering Method with a nonvanishing boundary condition, we
obtain an explicit breather solution with nonzero vacuum parameter b of the focusing …

We present ill-posedness results for the initial value problem (IVP) for the Gardner equation.
We measure the regularity of the Cauchy problem in the classical Sobolev spaces Hs, and …

In this paper, we give a comprehensive account of several recent results on the stability of
nontrivial soliton structures for some well-known non periodic dispersive models. We will …

Consider the generalized Korteweg-de Vries (gKdV) equations with power nonlinearities $
q= 2, 3, 4\ldots $ in dimension $ N= 1$, and the Zakharov-Kuznetsov (ZK) model with integer …

We examine the form, properties, stability and evolution of doubly-connected (two-vortex)
relative equilibria in the single-layer mode. We also find that although conservative inviscid …

This paper is concerned with the coupled modified Korteweg-de Vries (cmKdV) equations.
We derive infinite conservation laws through the Lax pair of the cmKdV equations. Through …