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” …

The fourth-order 4 model extends the classical 4 model of quantum field theory to the fourth-
order case, but sharing the same kink solution. It is also the dispersive counterpart of the …

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 …

We study decay of small solutions of the Born-Infeld equation in 1+ 1 dimensions, a
quasilinear scalar field equation modeling nonlinear electromagnetism, as well as branes in …

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 study the Cauchy problem for the generalized Boussinesq equation with
initial data in modulation spaces M^ s _ p^ ′, q (R^ n), M p′, qs (R n), n ≥ 1. n≥ 1. After a …

Existence of almost automorphic solutions for abstract delayed differential equations is
established. Using ergodicity, exponential dichotomy and Bi-almost automorphicity on the …

In this paper, we show the local well-posedness of the generalized Boussinesq equation
(gBQ) in and obtain the global well-posedness, finite-time blowup and small initial data …

In this note we show that all small solutions of the BBM equation must decay to zero as
t→+∞ in large portions of the physical space, extending previous known results, and only …

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 …