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Publications [#244171] of Stephanos Venakides

Papers Published

  1. Buckingham, R; Venakides, S, Long-time asymptotics of the nonlinear Schrödinger equation shock problem, Communications on Pure & Applied Mathematics, vol. 60 no. 9 (2007), pp. 1349-1414, ISSN 0010-3640 [MR2337507], [doi]
    (last updated on 2017/12/18)

    The long-time asymptotics of two colliding plane waves governed by the focusing nonlinear Schrödinger equation are analyzed via the inverse scattering method. We find three asymptotic regions in space-time: a region with the original wave modified by a phase perturbation, a residual region with a one-phase wave, and an intermediate transition region with a modulated two-phase wave. The leading-order terms for the three regions are computed with error estimates using the steepest-descent method for Riemann-Hilbert problems. The nondecaying initial data requires a new adaptation of this method. A new breaking mechanism involving a complex conjugate pair of branch points emerging from the real axis is observed between the residual and transition regions. Also, the effect of the collision is felt in the plane-wave state well beyond the shock front at large times. © 2007 Wiley Periodicals, Inc.
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