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We establish improved uniform error bounds for the time-splitting methods for the long-time dynamics of the nonlinear Schr\"odinger equation (NLSE) with weak nonlinearity. By a new technique of regula...
I will report my recent joint work with Jacek Jendrej on muti-solitons to the Klein-Gordon equations including their asymptotic stability and classification.
Nonlinear dynamics play a prominent role in many domains and are notoriously difficult to solve. Whereas previous quantum algorithms for general nonlinear equations have been severely limited due to t...
The weak stability is an important issue in fluid dynamics. We will discuss the mathematical understudying of concentration phenomena in the framework of weak solutions with either critical or subcrit...
We introduce the notion of expanding cone of a noncompact simple Lie group. This allows us to extend several results in homogeneous dynamics to more general settings. We show how this notion is used i...
Hydrodynamic stability at high Reynolds number is a central topic in fluid mechanics. It is closely related to turbulence. Whereas the laminar velocity profile is linearly stable for all Reynolds numb...
In this talk, we investigate a stochastic nutrient-phytoplankton model which incorporates the effect of white noise on phytoplankton growth. The global existence and uniqueness of a positive solution,...
Community structure division is a crucial problem in the field of network data analysis. Algorithms based on Markov chains are easy to use and provide promising solutions for community detection. In a...
In this talk, I will discuss the dynamics near a shear flow when the Coriolis force is involved. Compared with the non-Coriolis case, the spectral properties of the linearized Euler operator change fu...
Natural and man-made inland waters represent globally significant sites of methane production and emit annually about 100 Tg of this potent GHG to the atmosphere. On the other hand, a large fraction o...
The Earthquake Engineering and Soil Dynamics Technical Committee of the Geo-Institute (G-I) of the American Society of Civil Engineers (ASCE) is organizing the 5th conference on Geotechnical Earthquak...
The appearance of nonlinear phenomena used to be perceived as dangerous, with a general tendency to avoid them or control them. This perception has led to intensive research using various approaches a...
In recent years there has been a growing interest towards the integrability of systems which, though not Hamiltonian, retain some link to—or common origin with—Hamiltonian systems. One such field is t...
The study of Hamiltonian dynamical systems plays a fundamental role in many different contexts, both in pure and applied mathematics. Indeed, most of the physical laws ruling our everyday lives --the ...
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