We address two pressing questions in the theory of the Korteweg–de Vries (KdV) equation.
First, we show the uniqueness of solutions to KdV that are merely bounded, without any …

We study the Cauchy problem for the KdV equation∂ tu− 6 u∂ xu+∂ x 3 u= 0 with almost
periodic initial data u (x, 0)= V (x). We consider initial data V, for which the associated …

We consider the KdV equation $\partial _t u+\partial^ 3_x u+ u\partial _x u= 0$ with quasi-
periodic initial data whose Fourier coefficients decay exponentially and prove existence and …

We establish precise spectral criteria for potential functions $ V $ of reflectionless
Schrödinger operators $ L_V=-\partial _x^ 2+ V $ to admit solutions to the Korteweg–de …

We consider Schrödinger operators on the real line with limit-periodic potentials and show
that, generically, the spectrum is a Cantor set of zero Lebesgue measure and all spectral …

We prove the local well-posedness for the Cauchy problem of the Korteweg--de Vries
equation in a quasi-periodic function space. The function space contains functions such that …

Given sufficiently regular data\textit {without} decay assumptions at infinity, we prove local
well-posedness for non-linear dispersive equations of the form\[\partial_t u+\mathsf A …

This paper studies the existence and uniqueness problem for the generalized Benjamin-
Bona-Mahony (gBBM) equation with quasi-periodic initial data on the real line. We obtain an …

We consider the Cauchy problem of nonlinear Schrödinger equations (NLS) with almost
periodic functions as initial data. We first prove that given a frequency set …

We consider the Cauchy problem for the defocusing nonlinear Schr\" odinger equations
(NLS) on the real line with a special subclass of almost periodic functions as initial data. In …