By Agrawal M.R., Tewari U.B.

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13) Симетрiйнi властивостi цього рiвняння дослiдженi в роботi [4]. Далi ми покажемо, що рiвняння (13) може допускати ще одне зображення алгебри Галiлея. I. I. Чопик Знайдемо максимальну алгебру iнварiантностi (МАI) рiвняння (11). Теорема 1. МАI рiвняння (11) задається таким набором базисних операторiв: 1) Xa(2) 2) Xa(1) = exp{βx0 }∂a Jab = xa ∂b − xb ∂a , M = exp{αx0 }∂u , (14) 2 ∂a + xa ∂u = exp{(α − β)x0 } при α = 2β; α − 2β P 0 = ∂0 , P0 , Xa(1) = exp{βx0 }∂a , Xa(2) = exp{βx0 }{2x0 ∂a + xa ∂u } при α = 2β.

Acad. , 1992, 66–68. 5. , A new renormalization scheme in the Landau–Ginzburg–Wilson model, Phys. Lett. A, 1984, 104, № 3, 135–139. 6. , On the physical branch of the exact (local) RG equation, Phys. Lett. A, 1991, 158, № 6. 300–306. 7. , Lie and Q-condtoonal symmetry and exact solutions of local Wilson renormalization group equation, in Symmetry Analysis of Equations of Mathematical Physics, Kiev, Inst. Math. Ukr. , 1992, 50–54. 8. , Подгрупповой анализ групп Галилея, Пуанкаре и редукция нелинейных уравнений, Киев, Наук.

1/2 1. Функцiї f1 = x1 , f2 = x21 , ω = x0 задовольняють систему (31). Редукована система ЗДР має вигляд ϕ˙ 2 + 4λϕ22 + 4α1 α2 = 0, 3λ ϕ1 = 3λ 4α2 , α2 = 0, λα2 > 0.

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A Characterization of a Class of [Z] Groups Via Korovkin Theory by Agrawal M.R., Tewari U.B.

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