On the solutions of the nonlinear Liouville hierarchy

Details On the solutions of the nonlinear Liouville hierarchy On the solutions of the nonlinear Liouville hierarchy

2007-01-02

arxiv.org/abs/math-ph/0701002v1

Physics

Mathematical Physics

9 pages

Scientific paper

10.1088/1751-8113/40/32/002

We investigate the initial-value problem of the non-linear Liouville hierarchy. For the general form of the interaction potential we construct an explicit solution in terms of an expansion over particle clusters whose evolution is described by the corresponding-order cumulant of evolution operators of a system of finitely many particles. For the initial data from the space of integrable functions the existence of a strong solution of the Cauchy problem is proved.

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