The Universal Gaussian in Soliton Tails

David A. Kessler; J. Schiff

The Universal Gaussian in Soliton Tails

David A. Kessler
, J. Schiff

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We show that in a large class of equations, solitons formed from generic initial conditions do not have infinitely long exponential tails, but are truncated by a region of Gaussian decay. This phenomenon makes it possible to treat solitons as localized, individual objects. For the case of the KdV equation, we show how the Gaussian decay emerges in the inverse scattering formalism.

Original language	American English
Pages (from-to)	7924-7927
Journal	Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)
Volume	58
State	Published - 1998

Cite this

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title = "The Universal Gaussian in Soliton Tails",

abstract = "We show that in a large class of equations, solitons formed from generic initial conditions do not have infinitely long exponential tails, but are truncated by a region of Gaussian decay. This phenomenon makes it possible to treat solitons as localized, individual objects. For the case of the KdV equation, we show how the Gaussian decay emerges in the inverse scattering formalism.",

author = "Kessler, \{David A.\} and J. Schiff",

year = "1998",

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T1 - The Universal Gaussian in Soliton Tails

AU - Kessler, David A.

AU - Schiff, J.

PY - 1998

Y1 - 1998

N2 - We show that in a large class of equations, solitons formed from generic initial conditions do not have infinitely long exponential tails, but are truncated by a region of Gaussian decay. This phenomenon makes it possible to treat solitons as localized, individual objects. For the case of the KdV equation, we show how the Gaussian decay emerges in the inverse scattering formalism.

AB - We show that in a large class of equations, solitons formed from generic initial conditions do not have infinitely long exponential tails, but are truncated by a region of Gaussian decay. This phenomenon makes it possible to treat solitons as localized, individual objects. For the case of the KdV equation, we show how the Gaussian decay emerges in the inverse scattering formalism.

UR - http://arxiv.org/abs/patt-sol/9803003

M3 - Article

VL - 58

SP - 7924

EP - 7927

JO - Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)

JF - Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)

ER -

The Universal Gaussian in Soliton Tails

Abstract

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