标题： 非正则（非Stäckel）R分离和波动方程的广义调制孤子 显示英文标题

标题： Non-regular (non-Stäckel) R-separation and general modulated soliton of wave equation

摘要： 我们提出了一类正交非正则坐标，这类坐标在Kalnins和Miller的意义上是正交非Stäckel的，它们在三维Helmholtz方程中是R可分离的。 一组参数曲面由平行的Dupin环面组成，另外两组由圆锥面组成。 这个坐标系被用来简化Friedlander在$E^3$中对波方程的一般“简单渐进解”（波方程的调制孤子）公式推导，并修正他论文中的一些错误。 论文的扩展版本即将发表。 显示英文摘要

摘要： We present a class of orthogonal non-regular in a sense of Kalnins and Miller (hence non-St\"ackel) coordinates which are R-separable in 3-dim. Helmholtz equation. One family of parametric surfaces consists of parallel Dupin cyclides, the other two consist of circular cones. This coordinate system is used to simplify derivation of Friedlander's formulae for a general "simple progressive solution of the wave equation" (modulated soliton of wave equation) in $E^3$ and to correct some errors of his paper. The extended version of the paper will be published soon.