TY - JOUR

T1 - Numerical simulation of the semi-classical limit of the focusing nonlinear Schrödinger equation

AU - Bronski, Jared C.

AU - Kutz, J. Nathan

N1 - Funding Information:
Using the IST, Lax and Levermore were able to show trat the solution U(x, t, E) converged strongly to the solution of the inviscid Burger’s equation -.___ ’ Corresponding author (jared@math.uiuc.edu) Acknowledges support from NSF Postdoctoral Fellowship (DMS-9407473) dur-nl:g the early part of this work. ’ Acknowledges support from the National Science Foundation (DMS-9802920)

PY - 1999/4/26

Y1 - 1999/4/26

N2 - We present a series of careful numerical experiments on the semi-classical limit of the focusing nonlinear Schrödinger equation. We observe the emergence of an ordered train of solitons, which was originally predicted by one of the authors based on a numerical and analytical study of the Zakharov-Shabat eigenvalue problem. The velocity and amplitude of the solitons in the train are in extremely good agreement with the predictions of the previous work. We also observe a difference in behavior between analytic and non-analytic initial data which suggests that, at least for certain initial data, the elliptic modulation equations are correct.

AB - We present a series of careful numerical experiments on the semi-classical limit of the focusing nonlinear Schrödinger equation. We observe the emergence of an ordered train of solitons, which was originally predicted by one of the authors based on a numerical and analytical study of the Zakharov-Shabat eigenvalue problem. The velocity and amplitude of the solitons in the train are in extremely good agreement with the predictions of the previous work. We also observe a difference in behavior between analytic and non-analytic initial data which suggests that, at least for certain initial data, the elliptic modulation equations are correct.

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U2 - 10.1016/S0375-9601(99)00133-4

DO - 10.1016/S0375-9601(99)00133-4

M3 - Article

AN - SCOPUS:0042781006

VL - 254

SP - 325

EP - 336

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

SN - 0375-9601

IS - 6

ER -