The concept of approximate symmetry is introduced. We describe all nonlinearities F (u) with which the non-linear wave equation 2u + λu 3 + εF (u) = 0 with a small parameter ε is approximately scale and conformally invariant. Some approximate solutions of wave equations in question are obtained using the approximate symmetry.
We construct a complete set ofG(1, 3)-inequivalent ansätze of codimension 1 for the Navier-Stokes (NS) field which reduce the ns equations to systems of ordinary differential equations (ODE). Having solved these ODEs we thereby obtain solutions of the NS equations. Formulae of group multiplication of solutions are given. Several non-Lie ansätze are discussed. where the functions f ab , g a and F , and new variable ω = ω(x) are determined by means of operators of three-dimensional subalgebras of AG(1, 3) (1.2). We consider
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.