Open AccessMadelung Representation for Complex Nonlinear D'Alembert Equations in n-Dimensional Minkowski Space
Author(s) -
Norbert Euler,
M. Euler
Publication year - 1995
Publication title -
journal of nonlinear mathematical physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.544
H-Index - 40
eISSN - 1776-0852
pISSN - 1402-9251
DOI - 10.2991/jnmp.1995.2.3-4.9
Subject(s) - minkowski space , mathematics , nonlinear system , mathematical analysis , mathematical physics , phase space , hamiltonian (control theory) , amplitude , physics , quantum mechanics , mathematical optimization
The Madelung representation = uexp(iv) is considered for the d'Alembert equa- tion 2n F(| |) = 0 to develop a technique for finding exact solutions. We classify the nonlinear function F for which the amplitude and phase of the d'Alembert equa- tion are related to the solutions of the compatible d'Alembert-Hamiltonian system. The equations are studied in n-dimensional Minkowski space. We consider the following general nonlinear d'Alembert equation
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