Research
Research
Research
Research
1,105+ 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…
In this paper, we introduce the concepts of the $u$-bracket, finite multiple harmonic $u$-series, and $u$-multiple zeta values via the Carlitz module. These objects serve as function field counterpart…
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 …
The classical Goodstein process, defined via hereditary base-$k$ exponential normal form, is a well-known example of a principle unprovable in Peano Arithmetic. In this paper, we generalize this frame…
Bohr's last problem (1952) asks whether every ordinary Dirichlet series with nonzero Lindel\"of order function $\mu$ has $\mu'(\omega_\mu{-}0)\le-1$; a negative answer would imply Lindel\"of for $\zet…
Hochman asked whether there exists a cellular automaton $F$ such that every cellular automaton is a factor of $F$ in the dynamical sense. In particular, we do not require the factor map to commute wit…
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…
Recent developments in motivic homotopy theory, especially the construction of norm functors by Bachmann and Hoyois, rely heavily on the machinery of infinite categories. In this paper, we take a pure…
We show that the nonlocal Fisher information - defined as the entropy dissipation of the Boltzmann entropy for nonlocal heat equations - admits a natural lifting in the sense of Guillen and Silvestre …
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…
If totally periodic points are dense in a subshift $X$, its automorphism group is residually finite. We show a weak converse: if periodic points are not dense in a subshift $X$, then the automorphism …
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…
Free open-access publishing with Google Scholar indexing.
Submission Guide →