Newton's law for a trajectory of concentrationof solutions to nonlinear Schrodinger equation

Anatoli Babin; Alexander Figotin

doi:10.3934/cpaa.2014.13.1685

Article Contents

2014, Volume 13, Issue 5: 1685-1718. Doi: 10.3934/cpaa.2014.13.1685

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Newton's law for a trajectory of concentration of solutions to nonlinear Schrodinger equation

Anatoli Babin^1, and
Alexander Figotin^1,

1.
Department of Mathematics, University of California at Irvine, Irvine, CA 92697-3875

Received: November 30, 2013

Revised: December 31, 2013

Published: August 2015

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Abstract

One of important problems in mathematical physics concerns derivation of point dynamics from field equations. The most common approach to this problem is based on WKB method. Here we describe a different method based on the concept of trajectory of concentration. When we applied this method to nonlinear Klein-Gordon equation, we derived relativistic Newton's law and Einstein's formula for inertial mass. Here we apply the same approach to nonlinear Schrodinger equation and derive non-relativistic Newton's law for the trajectory of concentration.

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Mathematics Subject Classification: Primary: 35Q55, 35Q60, 35Q70; Secondary: 70S05, 78A35.

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