Nonlinear Waves Seminar

Amir Sagiv, Department of Applied Mathematics, Columbia University Floquet Hamiltonians - effective gaps and resonant decay Floquet topological insulators are an emerging category of materials whose properties are transformed by time-periodic forcing. Can their properties be understood from their first-principles continuum models, i.e., from a driven Schrodinger equation? First, we...

Igor Rumanov, Department of Applied Mathematics, University of Colorado Boulder (2+1)-dimensional Whitham systems: 2dNLS and KP vs. ‘hydrodynamic’ systems in one and two spatial dimensions The main result of this talk is the recently obtained Whitham modulation system for the (2+1)-dimensional nonlinear Schroedinger equation (2dNLS) (joint work with M. J...

Samuel Ryskamp, Department of Applied Mathematics, University of Colorado Boulder Modulation theory for Miles resonance and Mach reflection Mach reflection occurs when a sufficiently large amplitude line soliton interacts with a barrier at a sufficiently small angle. A Y-shaped resonant triad is then formed consisting of two smaller amplitude solitons...

Yi Zhu, Department of Mathematical Sciences, Tsinghua University, China Three-fold Weyl points for the periodic Schrödinger operator Weyl points are degenerate points on the spectral bands at which energy bands intersect conically. They are the origins of many novel physical phenomena and have attracted much attention recently. In this talk,...

Patrick Sprenger, Department of Mathematics, North Carolina State University Traveling wave solutions of the Kawahara equation The Kawahara equation is an asymptotic model of weakly nonlinear wave phenomena when third and fifth order dispersion are in balance. The model equation consists of the Korteweg-de Vries equation with an additional fifth-order...

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...

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...

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...

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...

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...