## 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...

## Nonlinear Waves Seminar - Mark Siemens

Jan. 22, 2019

Quantum Turbulent Structure in Light The infinite superpositions of random plane waves are known to be threaded with vortex line singularities which form complicated tangles and obey strict topological rules. We observe that within these structures a timelike axis appears to emerge with which we can define vortex velocities in...

## Nonlinear Waves Seminar - Patrick Sprenger

Nov. 6, 2018

Computing traveling wave solutions of the fifth order Korteweg-de Vries equation through Whitham theory Whitham modulation theory is a useful tool for describing the adiabatic evolution of periodic solutions to nonlinear dispersive equations. Modulation theory yields a first order system of quasilinear partial differential equations which describe the evolution of...

## Nonlinear Waves Seminar - Lev Ostrovsky

Oct. 23, 2018

Nonlinear waves in rotating fluids In this presentation the non-trivial dynamics of nonlinear dispersive waves affected by the Coriolis force is discussed. Applications include surface and internal waves in the ocean, magnetic sound in plasma, and other phenomena. The corresponding model equation (rKdV equation) derived by the author has the...