Journal of Nonlinear Mathematical Physics

Volume 14, Issue 2, April 2007

1. Approximate Lie symmetries of the Navier-Stokes equations

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 Navier-Stokes...

2. On a class of mappings between Riemannian manifolds

Thomas H OTWAY
Pages: 164 - 173
Effects of geometric constraints on a steady flow potential are described by an elliptic- hyperbolic generalization of the harmonic map equations. Sufficient conditions are given for global triviality.

3. A note on Bernoulli polynomials and solitons

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 terms of the Bernoulli polynomials...

4. On sl(2)-equivariant quantizations

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...

5. A multidimensional superposition principle: numerical simulation and analysis of soliton invariant manifolds I

Alexander A ALEXEYEV
Pages: 188 - 229
In the framework of a multidimensional superposition principle involving an analytical approach to nonlinear PDEs, a numerical technique for the analysis of soliton invari- ant manifolds is developed. This experimental methodology is based on the use of computer simulation data of soliton–perturbation...

6. A supersymmetric second modified KdV equation

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.

7. Resolving of discrete transformation chains and multisoliton solution of the 3-wave problem

Pages: 238 - 249
The chain of discrete transformation equations is resolved in explicit form. The new found form of solution alow to solve the problem of interrupting of the chain in the most strigtforward way. More other this form of solution give a guess to its generalization on the case of arbitrary semisimple algebra...

8. p-adic interpolating function associated with Euler numbers

Taekyun KIM, Daeyeoul KIM, Ja Kyung KOO
Pages: 250 - 257
In this paper, we investigate some relations between Bernoulli numbers and Frobenius- Euler numbers, and we study the values for p-adic l -function.

9. Construction of q-discrete two-dimensional Toda lattice equation with self-consistent sources

Hong-Yan WANG, Xing-Biao HU, Hon-Wah TAM
Pages: 258 - 268
The q-discrete two-dimensional Toda lattice equation with self-consistent sources is presented through the source generalization procedure. In addition, the Gramm- type determinant solutions of the system are obtained. Besides, a bilinear B ̈acklund transformation (BT) for the system is given.

10. Rota-Baxter operators on pre-Lie algebras

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 (the...

11. The Riccati and Ermakov-Pinney hierarchies

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 from...