Nonlinear Waves Seminar - Thibault Congy

Sept. 21, 2021

Speaker: Dr. Thibault Congy Affiliation: University of Northumbria, Newcastle, UK Title: Dispersive Riemann problem for the Benjamin-Bona-Mahony equation Abstract: The Benjamin-Bona-Mahony (BBM) equation $u_t + uu_x = u_{xxt}$ as a model for unidirectional, weakly nonlinear dispersive shallow water wave propagation is asymptotically equivalent to the celebrated Korteweg-de Vries (KdV) equation...

Nonlinear Waves Seminar - Justin Cole

Sept. 14, 2021

Justin Cole, Department of Mathematics, University of Colorado Colorado Springs Transverse Instability of Rogue Waves Rogue waves, or “freak waves”, are large amplitude waves that suddenly appear and then disappear. Originally the subject of folklore, these waves have now been successfully observed in numerous physical systems such as deep water...

Nonlinear Waves Seminar - Sean Nixon

Sept. 7, 2021

Sean Nixon, Department of Applied Mathematics, University of Colorado Boulder Analytical study of Floquet topological insulators The search for novel phenomena in photonic waveguides centers on engineering systems that feature unique dispersive properties often involving spectral degeneracies. From optical graphene to unidirectional invisibility to the anomalous quantum Hall effect, spectral...

Nonlinear Waves Seminar - Vera Hur

Feb. 25, 2020

Vera Hur, Department of Mathematics, University of Illinois Stokes waves in a constant vorticity flow: theory and numerics Stokes in the 1800s made many contributions about periodic waves at the surface of water, under the influence of gravity, propagating in permanent form a long distance at a practically constant velocity...

Nonlinear Waves Seminar - Thibault Congy

Feb. 4, 2020

Thibault Congy; Department of Mathematics, Physics, and Electrical Engineering; University of Northumbria; Newcastle, UK Bidirectional soliton gas The soliton structure plays a fundamental role in many physical systems due to its fundamental feature: its shape remains unchanged after the collision with another soliton in the case of integrable dynamics. Such...

Nonlinear Waves Seminar - Nalini Joshi

Jan. 21, 2020

Nalini Joshi, Department of Mathematics, Sydney University When Applied Mathematics Collided with Algebra Imagine walking from one tile to another on a lattice defined by reflections associated with an affine Coxeter or Weyl group. Examples include triangular or hexagonal lattices on the plane. Recently, it was discovered that translations on...

Nonlinear Waves Seminar - Justin Cole

Dec. 10, 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 - 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)...

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