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...
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...
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,...
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...
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...
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...