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In laboratory studies and numerical simulations, we observe clear signatures of unstable time-periodic solutions in a moderately turbulent quasi-two-dimensional flow. We validate the dynamical relevance of such solutions by demonstrating…
In 1908 Henri Poincar\'e gave a series of 'forgotten lectures' on wireless telegraphy in which he demonstrated the existence of a stable limit cycle in the phase plane. In 1929 Aleksandr Andronov published a short note in the Comptes Rendus…
The purpose of this article is to provide a perspective -- admittedly, a rather subjective one -- of recent developments at the interface of machine learning/data-driven methods and nonlinear wave studies. We review some recent pillars of…
In this paper, we are interested in studying the modulational dynamics of interfacial waves rising buoyantly along a conduit of a viscous liquid. Formally, the behavior of modulated periodic waves on large space and time scales may be…
These are notes of lectures on spinning particles and the worldline formalism originally given by Olindo Corradini and Christian Schubert at the School on Spinning Particles in Quantum Field Theory: Worldline Formalism, Higher Spins, and…
In recent papers (arXiv:2407.16507, arXiv:2408.05158) we presented results suggesting the existence of a new class of time-periodic solutions to the defocusing cubic wave equation on a one-dimensional interval with Dirichlet boundary…
This text is a slightly edited version of lecture notes for a course I gave at ETH, during the Summer term 2001, to undergraduate Mathematics and Physics students. It covers a few selected topics from perturbation theory at an introductory…
The diffusive viscous wave equation describes wave propagation in diffusive and viscous media. Examples include seismic waves traveling through the Earth's crust, taking into account of both the elastic properties of rocks and the…
An investigation of strongly interacting matter equation of state remains one of the major tasks of modern high energy nuclear physics for almost a quarter of century. The present work is my doctor of science thesis which contains my…
In this paper, we consider a wave equation with strong damping and logarithmic nonlinearity. This paper aims to study the local and global existence, uniqueness and the uniform energy decay rate of a weak solution under some sufficient…
In this work we discuss an approximate model for the propagation of deep irrotational water waves, specifically the model obtained by keeping only quadratic nonlinearities in the water waves system under the Zakharov/Craig-Sulem…
In this paper we first study the fixed-time stabilizability of discrete-time switched linear control systems. Using a geometric approach, we derive conditions under which such systems can be stabilized within a prescribed number of steps,…
The question of what conditions should be set at the nodes of a discrete graph for the wave equation with discrete time is investigated. The variational method for the derivation of these conditions is used. A parallel with the continuous…
These notes record the lectures for the CIME Summer Course taught by the first author in Cetraro during the week of June 19-23, 2017. The notes contain the proofs of several results on the classification of stable solutions to some…
This paper is concerned with the inverse scattering problem involving the time-domain elastic wave equations in a bounded $d$-dimensional domain. First, an explicit reconstruction formula for the density is established by means of the…
This material complements David Chandler's Introduction to Modern Statistical Mechanics (Oxford University Press, 1987) in a graduate-level, one-semester course I teach in the Department of Chemistry at Duke University. Students enter this…
Three-dimensional equatorial trapped waves excited by stellar isolation and the resulting equatorial superrotating jet in a vertical stratified atmosphere of a tidally-locked hot Jupiter are investigated. Taking the hot Jupiter HD 189733b…
The dispersing equation was derived from system of the hydrodynamic equations that take into account the gravity, and from boundary conditions of shock front. The dispersing equation made it possible to study unstable stability of front not…
The discrete multiscale analysis for boundary value problems in nonlinear discrete systems leads to a first order discrete modulational instability above a threshold amplitude for wave numbers beyond the zero of group velocity dispersion.…
In this paper, we propose a novel approach for controlling surface water waves and their interaction with floating bodies. We consider a floating target rigid body surrounded by a control region where we design three control strategies of…