A number of "truncated" problems are formulated and numerically studied to model the axial solutions to the nonlinear systems of equations describing the spatial axially symmetric laser-plasma interactions. It is shown that the proposed approach is well-posed and numerically efficient. This work was supported by the Russian Foundation for Basic Research (project N. 09-01-00625a).

Keywords: plasma oscillations, wake waves, axial solutions, finite difference method

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