id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-6012	Hussain, Akhtar; Usman, M.; Zidan, Ahmed M.; Herrera, Jorge	Unraveling Symmetry Properties in a Three-Dimensional Nonlinear Evolution Model via the Lie Group Method	2025	20	.pdf	application/pdf	6818	320	71	= 1 2 (ψxx − 2ψ3)x + 3 2 ( − 1 4 ∂−1 x ψyy + ψψy ) , ψt = −1 4 (ψxx − 2ψ3)x − 3 4 ( 1 4 ∂−1 x ψyy + ψx∂ −1 x ψy ) , ψt = 2(ψxx − 2ψ3)x − 3 4 ( ∂−1 x ψyy − 2ψx∂ −1 x ψy − 6ψψy ) , (1) where ∂−1 x is the inverse of ∂x with ∂−1 x ∂x = ∂x∂ −1 x = 1, and (∂−1 x g)(x) = ∫ =− avzux + avuxz.	cache/ejpam-6012.pdf	txt/ejpam-6012.txt