Journal of Nonlinear Mathematical Physics

Volume 5, Issue 3, August 1998

1. On Integrability of a (2+1)-Dimensional Perturbed KdV Equation

S.Yu. SAKOVICH
Pages: 230 - 233
A (2+1)-dimensional perturbed KdV equation, recently introduced by W.X. Ma and B. Fuchssteiner, is proven to pass the Painlevé test for integrability well, and its 4×4 Lax pair with two spectral parameters is found. The results show that the Painlevé classification of coupled KdV equations by A. Karasu...

2. Similarity Reductions for a Nonlinear Diffusion Equation

M.L. GANDARIAS, P. VENERO, J. RAMIREZ
Pages: 234 - 244
Similarity reductions and new exact solutions are obtained for a nonlinear diffusion equation. These are obtained by using the classical symmetry group and reducing the partial differential equation to various ordinary differential equations. For the equations so obtained, first integrals are deduced...

3. Quantum Differential Forms

Boris A. KUPERSHMIDT
Pages: 245 - 288
Formalism of differential forms is developed for a variety of Quantum and noncommutative situations.

4. A Solvable Many-Body Problem in the Plane

F. CALOGERO
Pages: 289 - 293
A solvable many-body problem in the plane is exhibited. It is characterized by rotation-invariant Newtonian ("acceleration equal force") equations of motion, featuring one-body ("external") and pair ("interparticle") forces. The former depend quadratically on the velocity, and nonlinearly on the coordinate,...

5. Matrix Exponential via Clifford Algebras

Rafal ABLAMOWICZ
Pages: 294 - 313
We use isomorphism between matrix algebras and simple orthogonal Clifford algebras C (Q) to compute matrix exponential eA of a real, complex, and quaternionic matrix A. The isomorphic image p = (A) in C (Q), where the quadratic form Q has a suitable signature (p, q), is exponentiated modulo a minimal...

6. Application of the Group-Theoretical Method to Physical Problems

Mina B. ABD-EL-MALEK
Pages: 314 - 330
The concept of the theory of continuous groups of transformations has attracted the attention of applied mathematicians and engineers to solve many physical problems in the engineering sciences. Three applications are presented in this paper. The first one is the problem of time-dependent vertical...

7. Some Homogenization and Corrector Results for Nonlinear Monotone Operators

Peter WALL
Pages: 331 - 348
This paper deals with the limit behaviour of the solutions of quasi-linear equations of the form - div (a (x, x/h, Duh)) = fh on with Dirichlet boundary conditions. The sequence (h) tends to 0 and the map a(x, y, ) is periodic in y, monotone in and satisfies suitable continuity conditions. It is...