Nonlinear Waves Seminar

Many-body quantum chaos of ultracold atoms in a quantum ratchet There are now over 200 quantum simulators on at least 8 separate architectures with long coherence times and controlled dynamics. These experimental systems have generated tremendous excitement about driven interacting quantum systems resulting in physics ranging from time crystals to...

New Integrals of Motion and Singularities in 2D Fluid Dynamics with Free Surface We study the problem of 2D incompressible fluid dynamics with free surface, we assume the the fluid is ideal and the flow is potential. Following the conformal mapping technique we reformulate the problem to surface variables and...

The Role of Topology in Magnetic Solitary Wave Dynamics Topological solitary waves have recently attracted attention from applied mathematics and physics communities for both technological applications and novel phenomena. In the field of ferromagnetism, topological structures include the one-dimensional topological bion and the two-dimensional skyrmion. The topology is the result...

Geometry of Discrete Integrable Systems Many interesting examples of discrete integrable systems can be studied from the geometric point of view. In this talk we will consider two classes of examples of such system: autonomous (QRT maps) and non-autonomous (discrete Painlevé equations). We introduce some geometric tools to study such...

Nonlinear stage of modulational instability, solitons and coherent structures Modulational instability (or MI, a.k.a. the Benjamin-Feir instability in deep water waves), is the instability of a constant background to long-wavelength perturbations, and is a ubiquitous nonlinear phenomenon which arises in many different physical contexts. Even though MI was discovered in...

An introduction to absorbing layers and non-reflecting boundary conditions. I will give an overview of different techniques to truncate unbounded domains by absorbing layers and non-reflecting or artificial boundary conditions. Among other topics I will describe the perfectly matched layer (PML) introduced in 1994 by Berenger (cited >10,000 times on...

Nick Ercolani, Department of Mathematics, University of Arizona Patterns, Defects and Phase Singularities The topic of this talk concerns understanding defect formation in spatially extended pattern-forming systems (such as Rayleigh-Benard Convection) that are far from equilibrium. We view these defects as coherent structures describable in terms of a phase order...

Wednesday, May 18, 2016 3:00 PM - 4:00 PM Main Campus - Engineering Office Tower - 226: Applied Math Conference Room Main Campus - Engineering Classroom Wing - 257: Newton Lab Alexei Cheviakov, Department of Mathematics and Statistics, University of Saskatchewan, Canada Exact Solutions of a Fully Nonlinear Two-Fluid Model...

Event Description: Igor Rumanov, Department of Applied Mathematics, University of Colorado Boulder A universal asymptotic regime in (2+1)-D hyperbolic nonlinear Schroedinger equation. Using numerical computations and analytical considerations based on similarity solutions, we demonstrate the appearance of a certain long-time regime in the (2+1)-dimensional hyperbolic nonlinear Schroedinger equation (HNLS). This...

Event Description: Matthew Turner, Department of Mathematics, University of Surrey Time-dependent conformal mappings with applications to nonlinear sloshing problems In this talk we examine two key features of time-dependent conformal mappings in doubly-connected regions, the evolution of the conformal modulus, Q(t), and the boundary transformation generalizing the Hilbert transform. Results...