Pages: 321 - 329
Charpit's method of compatibility and the method of nonclassical contact symmetries
for first order partial differential equation are considered. It is shown that these two
methods are equivalent as Charpit's method leads to the determining equations arising
from the method of nonclassical contact...
Pages: 330 - 341
We investigate a propagation of solitons for nonlinear Schrödinger equation under
small driving force. The driving force passes through the resonance. The process
of scattering on the resonance leads to changing of number of solitons. After the
resonance the number of solitons depends on the amplitude...
Pages: 342 - 347
We give a simple proof that for any non-zero initial data, the solution of the CamassHolm equation loses instantly the property of being compactly supported.
Pages: 348 - 380
) be the space of tensor densities of degree (or weight) on the circle S1
The space Dk
) of k-th order linear differential operators from F(S1
) to Fµ(S1
is a natural module over Diff(S1
), the diffeomorphism group of S1
. We determine
the algebra of symmetries of the modules...
Pages: 381 - 408
The differential-geometric and topological structure of Delsarte transmutation opertors their associated Gelfand-Levitan-Marchenko type equations are studied making
use of the de Rham-Hodge-Skrypnik differential complex. The relationships with spetral theory and special Berezansky type congruence properties...
Pages: 409 - 431
In this paper I study the functional representation of the Volterra hierarchy (VH).
Using the Miwa's shifts I rewrite the infinite set of Volterra equations as one functional
equation. This result is used to derive a formal solution of the associated linear
problem, a generating function for the conservation...
Pages: 432 - 448
We consider a nearest-neighbor hard-core model, with three states , on a homogeneous
Cayley tree of order k (with k + 1 neighbors). This model arises as a simple example
of a loss network with nearest-neighbor exclusion. The state (x) at each node x of
the Cayley tree can be 0, 1 and 2. We have Poisson...
Pages: 449 - 456
An implicit solution to the vanishing of the so-called Universal Field Equation, or
Bordered Hessian, which dates at least as far back as 1935  is revived, and derived
from a much later form of the solution. A linear ansatz for an implicit solution of
second order partial differential equations,...