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

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


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