Symmetry groups and spiral wave solution of a wave propagation equation

doi:10.1088/1009-1963/11/3/301

中国物理B ›› 2002, Vol. 11 ›› Issue (3): 207-212.doi: 10.1088/1009-1963/11/3/301

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Symmetry groups and spiral wave solution of a wave propagation equation

屈长征¹, 张全举²

(1)Institute of Modern Physics, Northwest University, Xi'an 710069, China; (2)School of Science, Xidian University 710071, Xi'an, China

收稿日期:2001-09-20 修回日期:2001-11-03 出版日期:2002-03-13 发布日期:2005-06-13
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No 19901027).

Symmetry groups and spiral wave solution of a wave propagation equation

Zhang Quan-Ju (张全举)^a, Qu Chang-Zheng (屈长征)^b

^a School of Science, Xidian University 710071, Xi'an, China; ^b Institute of Modern Physics, Northwest University, Xi'an 710069, China

Received:2001-09-20 Revised:2001-11-03 Online:2002-03-13 Published:2005-06-13
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No 19901027).

摘要/Abstract

摘要： We study a third-order nonlinear evolution equation, which can be transformed to the modified KdV equation, using the Lie symmetry method. The Lie point symmetries and the one-dimensional optimal system of the symmetry algebras are determined. Those symmetries are some types of nonlocal symmetries or hidden symmetries of the modified KdV equation. The group-invariant solutions, particularly the travelling wave and spiral wave solutions, are discussed in detail, and a type of spiral wave solution which is smooth in the origin is obtained.

Abstract: We study a third-order nonlinear evolution equation, which can be transformed to the modified KdV equation, using the Lie symmetry method. The Lie point symmetries and the one-dimensional optimal system of the symmetry algebras are determined. Those symmetries are some types of nonlocal symmetries or hidden symmetries of the modified KdV equation. The group-invariant solutions, particularly the travelling wave and spiral wave solutions, are discussed in detail, and a type of spiral wave solution which is smooth in the origin is obtained.

Key words: Symmetry group, optimal system, wave propagation, spiral wave

中图分类号: (Lie algebras of Lie groups)

02.20.Sv

02.30.Uu (Integral transforms)

张全举, 屈长征. Symmetry groups and spiral wave solution of a wave propagation equation[J]. 中国物理B, 2002, 11(3): 207-212.

Zhang Quan-Ju (张全举), Qu Chang-Zheng (屈长征). Symmetry groups and spiral wave solution of a wave propagation equation[J]. Chinese Physics, 2002, 11(3): 207-212.

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Symmetry groups and spiral wave solution of a wave propagation equation

Symmetry groups and spiral wave solution of a wave propagation equation

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