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  1. No Access

    Article

    Ring models of binocular rivalry and fusion

    When similar visual stimuli are presented binocularly to both eyes, one perceives a fused single image. However, when the two stimuli are distinct, one does not perceive a single image; instead, one perceives ...

    Ziqi Wang, Wei Dai, David W. McLaughlin in Journal of Computational Neuroscience (2020)

  2. No Access

    Article

    On the stability of time-harmonic localized states in a disordered nonlinear medium

    We study the problem of localization in a disordered one-dimensional nonlinear medium modeled by the nonlinear Schrödinger equation. Devillard and Souillard have shown that almost every time-harmonic solution ...

    Jared C. Bronski, David W. McLaughlin, Michael J. Shelley in Journal of Statistical Physics (1997)

  3. No Access

    Chapter

    Homoclinic Orbits in a Four Dimensional Model of a Perturbed NLS Equation: A Geometric Singular Perturbation Study

    This paper contains a detailed and explicit study of an important mechanism leading to chaotic dynamics in a perturbation of the integrable nonlinear Schrödinger equation, a perturbation which contains dam**...

    David W. McLaughlin, E. A. Overman II, Stephen Wiggins, C. **ong in Dynamics Reported (1996)

  4. Book Series

    Surveys in Applied Mathematics

    Joseph B. Keller, David W. McLaughlin, George C. Papanicolaou

  5. No Access

    Book

    Surveys in Applied Mathematics

    Joseph B. Keller, David W. McLaughlin… in Surveys in Applied Mathematics (1995)

  6. No Access

    Chapter and Conference Paper

    Whiskered Tori and Chaotic Behavior in Nonlinear Waves

    Chaotic behavior in deterministic dynamical systems is an important phenomenon with many physical ramifications. In finite-dimensional settings this behavior is well understood, because of several fundamental ...

    David W. McLaughlin in Proceedings of the International Congress of Mathematicians (1995)

  7. No Access

    Chapter

    Whiskered Tori for Integrable Pde’s: Chaotic Behavior in Near Integrable Pde’s

    This article is a summary of our numerical and theoretical studies (which were done in various collaborations with Alan Bishop, Nick Ercolani, Greg Forest, and Steve Wiggins) of near integrable nonlinear wave ...

    David W. McLaughlin, Edward A. Overman II in Surveys in Applied Mathematics (1995)

  8. No Access

    Article

    Morse and Melnikov functions for NLS Pde's

    The theory of the focusing NLS equation under periodic boundary conditions, together with the Floquet spectral theory of its associated Zakharov-Shabat linear operator

    Y. Li, David W. McLaughlin in Communications in Mathematical Physics (1994)

  9. No Access

    Chapter

    Semiclassical Behavior in the NLS Equation: Optical Shocks - Focusing Instabilities

    We consider the semiclassical limit of the non-linear Schroedinger equation in both the defocusing and the focusing cases. We review the theory of the defocusing case, and verify it with numerical experiments....

    Jared C. Bronski, David W. McLaughlin in Singular Limits of Dispersive Waves (1994)

  10. No Access

    Chapter

    The Behavior of Solutions of the NLS Equation in the Semiclassical Limit

    We report a numerical and theoretical study of the generation and propogation of oscillations in the semiclassical limit (h → 0) of the Nonlinear Schrödinger equation. In a general setting of both dimension and n...

    Shan **, C. David Levermore, David W. McLaughlin in Singular Limits of Dispersive Waves (1994)

  11. No Access

    Chapter and Conference Paper

    Toward a Topological Classification of Integrable PDE’s

    We model Fomenko’s topological classification of 2 degree of freedom integrable stratifications in an infinite dimensional soliton system. Specifically, the analyticity of the Floquet discriminant Δ(q, ») in both...

    Nicholas M. Ercolani, David W. McLaughlin in The Geometry of Hamiltonian Systems (1991)

  12. No Access

    Chapter and Conference Paper

    On the Construction of a Modulating Multiphase Wavetrain for a Perturbed Kdv Equation

    This paper summarizes the status of a direct construction of an asymptotic representation of a modulating multiphase wavetrain for a class of perturbed kdV equations. This class includes the kdV-Burgers equati...

    David W. McLaughlin in Oscillation Theory, Computation, and Metho… (1986)

  13. No Access

    Chapter

    Solitary Waves as Fixed Points of Infinite Dimensional Maps

    Coherent structures which are localized in space arise and play important roles in turbulent fields. Examples include tornados, large vortices in a turbulent wake, and isolated vortices in the ocean. These coh...

    David W. McLaughlin, J. V. Moloney… in Nonlinear Electrodynamics in Biological Sy… (1984)

  14. No Access

    Chapter and Conference Paper

    An Overview of Soliton Mathematics

    I have been asked to provide some background about “soliton mathematics”. I will describe an overview of the subject which indicates how some of the different mathematical developments fit together and complim...

    David W. McLaughlin in Physics in One Dimension (1981)

  15. No Access

    Chapter and Conference Paper

    Some comments on Bäcklund transformations, canonical transformations, and the inverse scattering method

    Hermann Flaschka, David W. McLaughlin in Bäcklund Transformations, the Inverse Scat… (1976)