CAJ | 학술논문

万方数据

西北大学学报(自然科学版) 서북대학학보(자연과학판)
JOURNAL OF NORTHWEST UNIVERSITY(NATURAL SCIENCE EDITION)
2003年 4期 383-388 ,共6页

刘若辰%何文丽%张顺利%屈长征劉若辰%何文麗%張順利%屈長徵

류약신%하문려%장순리%굴장정

对称李群%最优系统%伴随表示%非线性发展方程對稱李群%最優繫統%伴隨錶示%非線性髮展方程
대칭리군%최우계통%반수표시%비선성발전방정
Lie group of symmetry%optimal system%adjoint representation%nonlinear evolution equation

系统地研究了来自于射影几何中平面曲线运动的1+1维非线性方程的对称代数.发现此方程有一个七维对称群并且其对称代数的一维最优子代数有21个元素,通过寻找在群的伴随作用下的代数不变量,证明了该最优系统的最优性.
계통지연구료래자우사영궤하중평면곡선운동적1+1유비선성방정적대칭대수.발현차방정유일개칠유대칭군병차기대칭대수적일유최우자대수유21개원소,통과심조재군적반수작용하적대수불변량,증명료해최우계통적최우성.
The symmetry algebras of 1+1 dimensional nonlinear evolution equation arising from the motion of plane curve in affine geometry are systematically studied.It is found that the equation admits a seven-dimensional symmetry group H1 and there are twenty-one elements in the one-parameter optimal system of the symmetry algebras.The optimality of one-parameter optimal system θ1 is established by finding some algebraic invariants under the ajoint actions of the group H1.