Travaux sur les symétries de Lie des équations aux ... - DMA - Ens

− 1 3+ 1 3− 1 4+ 1 4∑Hl k 1H k k,y+ 1 ∑H k l k 6 1L k k,k,x + 2 ∑Hl k 3 1G k M k,k +k12k15k20∑ ∑Hl k 1G p M k,p − 1 ∑ ∑Hl k 31Hp k L p k,k+ 1 ∑ ∑Hl k 31H p k Lk k,pk pk pk p2124∑ ∑Hl k 1H p k Lp p,p − 1 ∑ ∑+ 1 ∑Hl k 44 1L k k,k Θ0 l+k∑kp26H k l 1Θ 0 Θ k m− 1 2 Ll 1l1 ,l 1 ,x Θ0 g+kpH k l 1H p k Θp ηk6125−+ G l 1y l 1 Ll 1l1 ,l 1 3− 1 2 Hl 1l1 ,x Ll 1l1 ,l 1 6−− ∑ k+ 1 2G k L l 1l1 ,l 1L l 1l1 ,k∑k22+ 1 2∑kG k L l 1l1 ,l 1L k k,kG k L l 1l1 ,l 1Θ k − 1 4 Ll 1l1 ,l 1Θ 0 Θ 0 n+db+ 1 4∑kH k l 1H l 1kL l 1l1 ,l 127++ G l 1y l 1 Θl −1β1 2 Hl 1l1 ,x Θl 1− ∑ kG k L l 1l1 ,k Θl 1− 1 4 Θ0 Θ 0 Θ l 1+oζ+ 1 2−δ∑G k L k k,k Θl 1kc+ 1 4∑kH k l 1H l 1kΘ l 1θ+ 1 2∑G k Θ k Θ l 1−kf+ 1 3 Hl 1l 1 ,y l 1 Θ0 − 1h 6 Ll 1l1 ,l 1 ,x Θ0 g−− 2 3 Gl 1M l1 ,l 1Θ 0 − 1 ∑G k M l1 ,k Θ 0i 3ke+ 1 ∑Hl k 4 1L k k,k Θ0 + 1 ∑4klk+ 1 3∑kH l 1kL k l 1 ,l 1Θ 0 j− 1 3∑Hl k 1Θ 0 Θ k − 1 4 Ll 1l1 ,l 1Θ 0 Θ 0 − 1n 4 Θ0 Θ 0 Θ l 1.omAs usual, all the terms underlined with the 15 roman alphabetic lettersa, b, . . ., n, o appended vanish evidently. Furthermore, we claim that theeight terms underlined with the 8 Greek alphabetic letters α, β, γ, δ, ε, ζ, ηkH k l 1L l 1l1 ,k Θ0 k+