Extended rotation and scaling groups for nonlinear evolution equations

摘要: A (1+1)-dimensional nonlinear evolution equation is invariant under the rotation group if it infinitesimal generator V = x∂ u  − u∂ x . Then solution satisfies condition u x = −x/u. For equations that do not admit group, we provide an extension of group. The corresponding exact can be constructed via set R 0 = {u: u x = xF(u)} a contact first-order differential structure, where F smooth function to determined. time on R 0 shown governed by dynamical system. We introduce scaling groups characterized $$\tilde S_0 $$ depends two constants ∈ and n ≠ 1. When ∈ = 0, reduces S 0 introduced Galaktionov. also generalization both groups, which described E 0 with parameters b. a = 0 or b = 0, respectively S 0. These approaches are used obtain solutions reductions systems equations.