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

56just below). We obtain:(3.109)0 = 1 2 δj l 1L l 2− δ j l 2 ,l 2 ,y l 3 l 1M l2 ,l 3 ,x + 1a b 2 δj l 2L l 1− δ j l 1 ,l 1 ,y l 3 l 2M l1 ,l 3 ,x −c4− 1 2 δj l 1L l 3+ δ j l 3 ,l 3 ,y l 2 l 1M l3 ,l 2 ,x − 1d b 3 δj l 3L l 1+ δ j l 1 ,l 1 ,y l 2 l 3M l1 ,l 2 ,x +e3+ L j − L j + 1 l 1 ,l 2 ,y l 3 l 1 1 ,l 3 ,y l 2 2 2 δj l 1L l 3− 1 l 3 ,l 3 ,y l 2d 2 δj l 1L l 2+l 2 ,l 2 ,y l 3a+ 1 3 δj l 3L l 1− 1 l 1 ,l 1 ,y l 2e 2 δj l 2L l 1+l 1 ,l 1 ,y l 3c+ 1 2 Hj l 3M l1 ,l 2− 15 2 Hj l 2M l1 ,l 3+ 16 4 δj l 2L l 3l3 ,l 3L l 1l1 ,l 1− 1f 4 δj l 3L l 2l2 ,l 2L l 1l1 ,l 1g++ ∑ kL k l 1 ,l 3L j l 2 ,k− ∑ kL k l 1 ,l 2L j l 3 ,k+11+ 1 ∑2 δj l 3L k l 1 ,l 2L k k,kk+ 1 4 δj l 2L l 1l1 ,l 1Θ l 3jh12− 1 ∑2 δj l 2L k l 1 ,l 3L k k,kk− 1 4 δj l 3L l 1l1 ,l 1Θ l 2ki++ 1 4 δj l 2L l 3l3 ,l 3Θ l 1+ 1 ∑2 δj l 3L k l 1 ,l 2Θ k − 1 ∑2 δj l 2L k l 1 ,l 3Θ kknko++ 1 2 δj l 2M l1 ,l 3Θ 0 − 1p 2 δj l 3M l1 ,l 2Θ 0 + 1q 4 δj l 2Θ l 3Θ l 1− 1 ∑2 δj l 1Hl k 2M l3 ,kk− 1 4 δj l 1L l 2l2 ,l 2Θ l 3v8rl− 1 4 δj l 3L l 2l2 ,l 2Θ l 1− 1 4 δj l 3Θ l 2Θ l 1−s− 1 4 δj l 1L l 2l2 ,l 2L l 3l3 ,l 3+ 1 ∑t 2 δj l 1L l2 ,l 3L k k,k −ku+ 1 ∑2 δj l 1− 1 4 δj l 1L l 3l3 ,l 3Θ l 2− 1 2 δj l 1M l2 ,l 3Θ 0 y− 1 4 δj l 1Θ l 2Θ l 3− 1 ∑2 δj l 2Hl k 1M l3 ,kk− 1 4 δj l 2L l 1l1 ,l 1Θ l 3j10w−zkL k l 2 ,l 3Θ k x−− 1 4 δj l 2L l 1l1 ,l 1L l 3l3 ,l 3+ 1 ∑f 2 δj l 2L k l 1 ,l 3L k k,k −ki+ 1 ∑2 δj l 2L k l 1 ,l 3Θ k o−− 1 4 δj l 2L l 3l3 ,l 3Θ l 1− 1 2 δj l 2M l1 ,l 3Θ 0 p− 1 4 δj l 2Θ l 3Θ l 1l+rk+m