Journal of Nonlinear Mathematical Physics

Volume 12, Issue 3, August 2005

1. Nonclassical Contact Symmetries and Charpit's Method of Compatibility

Daniel J ARRIGO
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...

2. The Stimulated Scattering of Solitons on a Resonance

Sergei GLEBOV, Oleg KISELEV
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...

3. Compactly Supported Solutions of the Camassa-Holm Equation

David HENRY
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.

4. Symmetries of Modules of Differential Operators

H GARGOUBI, P MATHONET, V OVSIENKO
Pages: 348 - 380
Let F(S1 ) be the space of tensor densities of degree (or weight) on the circle S1 . The space Dk ,µ(S1 ) 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...

5. The Structure of Gelfand-Levitan-Marchenko Type Equations for Delsarte Transmutation Operators of Linear Multi-Dimensional Differential Operators and Operator Pencils. Part 2

Jolanta GOLENIA, Anatolij K PRYKARPATSKY, Yarema A PRYKARPATSKY
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...

6. Functional Representation of the Volterra Hierarchy

V E VEKSLERCHIK
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...

7. A Three State Hard-Core Model on a Cayley Tree

James MARTIN, Utkir ROZIKOV, Yuri SUHOV
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...

8. Implicit Solutions to Some Lorentz Invariant Nonlinear Equations Revisited

David B FAIRLIE
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 [1] 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,...