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” …

We show that the limit infimum, as time \,t\, goes to infinity, of any uniformly bounded in time
H^3/2+∩L^1 solution to the intermediate long wave (ILW) equation converges to zero …

We consider solutions to the initial value problem associated to the intermediate long wave
(ILW) equation. We establish persistence properties of the solution flow in weighted Sobolev …

Consider the Hamiltonian $ abcd $ system in one dimension, with data posed in the energy
space $ H^ 1\times H^ 1$. This model, introduced by Bona, Chen, and Saut, is a well-known …

In this paper we derive time-decay and Strichartz estimates for the generalized Benjamin-
Bona-Mahony equation on the framework of modulation spaces M p, q s. We use these …

In this paper, we consider globally defined solutions of Camassa–Holm (CH)-type equations
outside the well-known nonzero-speed, peakon region. These equations include the …

This paper aims to show that the Cauchy problem of the Burgers equation with a weakly
dispersive perturbation involving the Bessel potential (generalization of the Fornberg …

The generalized Benjamin-Bona-Mahony equation (gBBM) is a model for nonlinear
dispersive waves which, in the long-wave limit, is approximately equivalent to the …

We consider the decay problem for the generalized improved (or regularized) Boussinesq
model with power type nonlinearity, a modification of the originally ill-posed shallow water …

In this paper we prove that all small, uniformly in time $ L^ 1\cap H^ 1$ bounded solutions to
KdV and related perturbations must converge to zero, as time goes to infinity, locally in an …