Klein-Gordon 方程的指数局部化解
摘要
presented for the Klein-Gordon equation in two and three spatial dimensions. These solutions depend on four free parameters. For certain parameter relations, the solutions describe wave packets containing oscillations whose amplitudes decrease in a Gaussian manner with distance from a point moving at the group velocity along a straight line. The solutions are constructed using exact complex solutions of the eikonal equation and may be regarded as ray solutions with amplitudes involving a single term. It is also shown that the multidimensional nonlinear Klein-Gordon equation can be reduced to an ordinary differential equation with respect to the complex eikonal.
引用
@article{arxiv.0711.4143,
title = {Exponentially localized solutions of the Klein-Gordon equation},
author = {M. V. Perel and I. V. Fialkovsky},
journal= {arXiv preprint arXiv:0711.4143},
year = {2009}
}
备注
9 pages, 1 figure. Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 275, 2001, pp. 187--198 (in Russian)