Nonlinear Waves Seminar - Patrick Sprenger

Nov. 5, 2019

n Patrick Sprenger, Department of Applied Mathematics, University of Colorado Boulder Generalized Riemann problems in dispersive hydrodynamics Nonlinear, dispersive wave phenomena are observed in a variety of physical contexts in nature and the laboratory. Mathematically, the dynamics are described by a dispersive hydrodynamic system---conservation laws modified by dispersion. Oftentimes, a...

Nonlinear Waves Seminar - Justin Cole

Oct. 29, 2019

Justin Cole Department of Applied Mathematics, University of Colorado Boulder Soliton Dynamics in the Korteweg-de Vries Equation with Nonzero Boundary Conditions Inspired by recent experiments, the Korteweg-de Vries equation with nonzero Dirichlet boundary conditions is considered. Two types of boundary data are examined: step up (which generates a rarefaction wave)...

Nonlinear Waves Seminar - S. Chakravarty

Oct. 22, 2019

S. Chakravarty, Department of Mathematics, University of Colorado Colorado Springs A class of rational solutions of the KPI equation I will revisit a class of KP "lump" solutions which were studied by Ablowitz & Villarroel as rational potentials of the non-stationary Schroedinger equation. Unlike other KPI lump solutions (simple lumps)...

Nonlinear Waves Seminar - Patrick Weidman

Oct. 8, 2019

Patrick Weidman Department of Mechanical Engineering, University of Colorado Boulder Steady flow of one uniformly rotating fluid layer above another immiscible uniformly rotating fluid layer. The steady laminar flow of two immiscible, uniformly rotating fluid layers is studied and exact similarity solutions of the axisymmetric Navier-Stokes equations in cylindrical polar...

Nonlinear Waves Seminar - Igor Rumanov

April 23, 2019

Whitham theory and dispersive shock waves (DSWs) for the radial nonlinear Schroedinger (rNLS) equation. Dispersive shock waves of the defocusing rNLS equation in two spatial dimensions are studied. This equation arises naturally in Bose-Einstein condensates, water waves and nonlinear optics. A unified nonlinear WKB approach, equally applicable to integrable and...

Nonlinear Waves Seminar - Mingzhong Wu

April 9, 2019

Experimental Observation of Spin-Wave Fractals A fractal is a shape made of parts each of which is similar to the whole in some way. One can group fractals into two main categories, (i) exact fractals in which the same feature replicates itself on successively smaller scales and (ii) statistical fractals...

Nonlinear Waves Seminar - Igor Rumanov

March 13, 2019

Whitham modulation theory - developments and open problems I discuss the development of Whitham modulation theory as a nonlinear WKB method successfully used to describe the behavior of nonlinear dispersive waves. Recent advances include the appearance of the Whitham theory for (2+1)-dimensional evolution equations of Kadomtsev-Petviashvili (KP) type. The systems...

Nonlinear Waves Seminar - Mahmoud I. Hussein

Feb. 26, 2019

Generalized dispersion relation predicts harmonic generation in strongly nonlinear systems In recent work, we have derived an exact nonlinear dispersion relation for elastic wave propagation in a thin rod (linearly nondispersive) and a thick rod (linearly dispersive). The derivation is generally applicable to any type of nonlinearity, geometric (related to...

Nonlinear Waves Seminar - Justin Cole

Feb. 12, 2019

Topologically Protected Edge Modes in Longitudinally Driven Waveguides A tight-binding approximation is developed for deep longitudinally driven photonic lattices. The physical system considered is that of a laser-etched waveguide array which is helically-varying in the direction of propagation. Focus is placed on the so-called Lieb and Kagome lattices. The lattice...

Nonlinear Waves Seminar - Michelle Maiden

Jan. 29, 2019

Soliton fission from a large disturbance in the viscous fluid conduit system The resolution of a large, localized initial disturbance is considered in the context of the viscous fluid conduit system--the driven, cylindrical, free interface between two miscible Stokes fluids with high viscosity contrast. Due to buoyancy induced nonlinear self-steepening...

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