Journal of Non-linear Mathematical Physics

ISSN: 1402-9251
Volume 14, Issue 2, April 2007
V N GREBENEV, M OBERLACK
Pages: 157 - 163
In the framework of the theory of approximate transformation groups proposed by Baikov, Gaziziv and Ibragimov [1], the first-order approximate symmetry operator is calculated for the Navier-Stokes equations. The symmetries of the coupled system obtained by expanding the dependent variables of the...
Khristo N BOYADZHIEV
Pages: 174 - 178
The dependence on time of the moments of the one-soliton KdV solutions is given by Bernoulli polynomials. Namely, we prove the formula R x n sech 2 (x − t) dx = 2 π n (−i) n Bn ( 1 2 + t π i) , expressing the moments of the one-soliton function sech 2 (x−t) in...
S BOUARROUDJ, M Iadh AYARI
Pages: 179 - 187
By computing certain cohomology of Vect(M ) of smooth vector fields we prove that on 1-dimensional manifolds M there is no quantization map intertwining the action of non-pro jective embeddings of the Lie algebra sl(2) into the Lie algebra Vect(M ). Contrariwise, for pro jective embeddings sl(2)-equivariant...
Meng-Xia ZHANG, Q P LIU
Pages: 230 - 237
In this paper, based on the B Ãàacklund transformation for the supersymmetric MKdV equation, we propose a supersymmetric analogy for the second modified KdV equation. We also calculate its one-, two- and three-soliton solutions.
Xiuxian LI, Dongping HOU, Chengming BAI
Pages: 269 - 289
Rota-Baxter operators or relations were introduced to solve certain analytic and com- binatorial problems and then applied to many fields in mathematics and mathematical physics. In this paper, we commence to study the Rota-Baxter operators of weight zero on pre-Lie algebras. Such operators satisfy...
Marianna EULER, Norbert EULER, Peter LEACH
Pages: 290 - 310
The concept and use of recursion operators is well-established in the study of evolution, in particular nonlinear, equations. We demonstrate the application of the idea of recursion operators to ordinary differential equations. For the purposes of our demonstration we use two equations, one chosen...