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- Peter D. Miller, Spyridon Kamvissis
- 1998

We present numerical experiments that provide new strong evidence of the existence of the semiclassical limit for the focusing nonlinear SchrÃ¶dinger equation in one space dimension. Our experimentsâ€¦ (More)

- Peter D. Miller, Christopher K. R. T. Jones, A M Rogerson, Lawrence J. Pratt
- 1997

Geometric methods from dynamical systems are used to study Lagrangian transport in numerically-generated, time-dependent, two-dimensional vector elds. The ows analyzed here are numerical solutions toâ€¦ (More)

- Peter D. Miller
- 2004

The steepest descent method for asymptotic analysis of matrix Riemann-Hilbert problems was introduced by Deift and Zhou in 1993 [14]. A matrix Riemann-Hilbert problem is specified by giving a tripleâ€¦ (More)

- Spyridon Kamvissis, K T-R Mclaughlin, Peter D. Miller
- 2003

For COURSE PACK and other PERMISSIONS, refer to entry on previous page. For more information, send e-mail to permissions@pupress.princeton.edu University Press. All rights reserved. No part of thisâ€¦ (More)

We study the spectral stability properties of periodic traveling waves in the sine-Gordon equation, including waves of both subluminal and superluminal propagation velocities as well as waves of bothâ€¦ (More)

We present a detailed analysis of the solution of the focusing nonlinear SchrÃ¶dinger equation with initial condition Ïˆ(x, 0) = N sech(x) in the limit N â†’ âˆž. We begin by presenting new and moreâ€¦ (More)

We obtain Plancherel-Rotach type asymptotics valid in all regions of the complex plane for orthogonal polynomials with varying weights of the form eâˆ’NV (x) on the real line, assuming that V has onlyâ€¦ (More)

We present the results of a large number of careful numerical experiments carried out to investigate the way that the solution of the integrable focusing nonlinear Schrodinger equation with Â xedâ€¦ (More)

- Richard KollÃ¡r, Peter D. Miller
- SIAM Review
- 2014

Two concepts, evidently very different in nature, have proved to be useful in analytical and numerical studies of spectral stability in nonlinear wave theory: (i) the Krein signature of anâ€¦ (More)

- Peter D. Miller
- 2001

Many important problems in the theory of integrable systems and approximation theory can be recast as Riemann-Hilbert problems for a matrix-valued unknown. Via the connection with approximationâ€¦ (More)