Dispersive Regularization of Shocks

Abstract

In completed research: (a) We have tested, with positive results, the Ansatz that is used in the higher order Lax-Levermore theory developed by us (with T. Zhang). (b) We have shown the stability of solitary pulses through a semiconduction in the Gunn effect (with L.L. Bonilla). In on-going research: (a) we have established strong results (analytically and numerically) in the semifinite Toda chain with time-dependent (periodic) forcing. Our work here goes beyond integrable theory (with P. Deift and T. Kricherbauer). (b) We have observed numerically that certain spectra in nonintegrable cases remain fixed in some averaged sense (with M. McDonald). (c) We have made some progress in the longstanding problem of the initial-boundary value problem for the KdV equation (with A. Fokas). Dispersive shocks, Particle chain, Gunn effect.

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Document Details

Document Type
Technical Report
Publication Date
Aug 25, 1992
Accession Number
ADA257256

Entities

People

  • Stephanie Venakides

Organizations

  • Duke University

Tags

Communities of Interest

  • Advanced Electronics

DTIC Thesaurus Topics

  • Band Gaps
  • Band Structures
  • Boundaries
  • Boundary Value Problems
  • Eigenvalues
  • Energy Bands
  • Equations
  • Frequency
  • Gunn Effect
  • Inverse Scattering
  • Mathematics
  • Phase Shift
  • Scattering
  • Semiconductors
  • Solitons
  • Spectra
  • Waves

Fields of Study

  • Mathematics

Readers

  • Atmospheric Science / Meteorology, specifically Wind Wave Turbulence.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Research Science/Academic Research