Research
Research
Research
Research
824+ open-access research outputs.
We establish the approximate controllability in $L^2$ for the nonlinear Benjamin-Ono equation on torus via two-dimensional control input. Our proof is based on adaptations of geometric control approac…
Let $-\Delta_{\mathbb{H}}+V$ be the Schr\"odinger operator on $\mathbb{H}$ where $V \in L^p(\mathbb{H}) \cap L^\infty(\mathbb{H})$ for some $p > 0$. If $(X_n)$ is a uniformly discrete sequence of comp…
In this paper, we first extend the explicit formula \cite{gerard2023explicit} for the classical Benjamin-Ono equation to each flow of the Benjamin-Ono hierarchy on line. We then use this representatio…
We investigate the Benjamin-Feir instability of small-amplitude gravity-capillary Stokes waves in deep water for the full water wave equations. While modulational instability has been classically pred…
We develop a framework for the fifth-order Kadomtsev--Petviashvili equation on $\mathbb{T}_x \times \mathbb{R}_y$ within a mean-zero KP-adapted Sobolev scale. A localized high-order feedback acting on…
This article is concerned with Kronecker flows on the infinite torus. The work is partly motivated by the fact that many Hamiltonian PDEs and systems on infinite lattices admit invariant tori, of poss…
For first passage percolation (FPP) on Euclidean lattices $\mathbb{Z}^d$ with $d\ge 2$, it is expected that the variance of the first passage time between two points grows sublinearly in the distance …
We prove that for almost all symmetric spaces $X$ and for any sequence of compact locally symmetric spaces $Y_n$ which is uniformly discrete, has a uniform spectral gap, and converges in the sense of …
Nonlinear waves in dispersive media can be succeptible to modulational instabilities. We examine a category of scalar equations, with general dispersion and monomial nonlinearity, including a large va…
In this paper, we consider the one-dimensional generalized Benjamin--Bona--Mahony (gBBM) equation \[(1-\partial_x^2)u_t+(u+u^p)_x=0,\qquad p=2,3,4,\dots,\] posed either on the real line $\mathbb R$ or…
We construct a class of infinite-order multisoliton solutions of the Benjamin-Ono equation on the line, for which the initial data exhibits slow spatial decay. We prove that in the long-time asymptoti…
We study the spectral stability of small-amplitude Stokes waves in a family of weakly nonlinear, unidirectional models of the form $u_t + L u + (u^2)_x = 0$. We introduce a perturbation method to expa…
This paper is devoted to the numerical analysis of a fully discrete finite element approximation for the stochastic Benjamin-Bona-Mahony equation driven by multiplicative noise. We first establish the…
We consider the quintic generalized Benjamin-Bona-Mahony equation $$ u_t-u_{xxt} + \partial_x\big(u + u^{5}\big)= 0,\qquad (t,x)\in \mathbb{R}_+ \times \mathbb{R}. $$ Using the space-time resonance …
We study the modulational instability of smooth, small-amplitude periodic traveling wave solutions to the $b$-family of Novikov equation with cubic nonlinearity with an arbitrary coefficient $b>0$. Ou…
Let $V \subset \mathbb{R}$ be a finite set with $|V| = n $ and suppose we are given each pairwise distance independently with probability $p$. We show that if $p = (1+\epsilon)/n$, for some fixed $\ep…
We consider the half-wave maps equation $$ \partial_t \mathbf{u} = \mathbf{u} \times |D| \mathbf{u} $$ for $\mathbf{u} : \mathbb{R} \times \mathbb{T} \to \mathbb{S}^2$, where $\mathbb{T}=\mathbb{R}/2 …
By developing discrete counterparts to recent advances in nonlinear integrability, and in particular to the discovery of explicit formulas, we design and analyze fully-discrete approximations to the B…
We prove that random triangulations of high genus contain very large expander subgraphs, answering a question of Benjamini. Our approach relies on new general criteria for arbitrary graphs to contain …
In this manuscript, we would established in low regularity spaces $H^\ell, \ell\in [0,1)$, the existence and stability results of time-periodic solution of 1D Cauchy problem of forced damped Benjamin-…
Free open-access publishing with Google Scholar indexing.
Submission Guide →