An eigenvalue problem with a reference function and the corresponding hierarchy
of nonlinear evolution equations are proposed. The bi-Hamiltonian structure of the
hierarchy is established by using the trace identity. The isospectral problem is nonlinearized as to be finite-dimensional completely integrable...
The two-dimensional unsteady coupled Burgers' equations with moderate to severe
gradients, are solved numerically using higher-order accurate finite difference schemes;
namely the fourth-order accurate compact ADI scheme, and the fourth-order accurate
Du Fort Frankel scheme. The question of numerical...
A number of important results of studying large deformations of hyper-elastic shells
are obtained using discrete methods of mathematical physics . In the present
paper, using the variational method for solving nonlinear boundary problems of statics
of hyper-elastic membranes under the regular...
Symmetry classification of two-body central potentials in a two-particle Schrödinger
equation in terms of contact transformations of the equation has been investigated.
Explicit calculation has shown that they are of the same four different classes as
for the point transformations. Thus in this problem...
In this paper we study symmetry reductions of a class of nonlinear fourth order partial
utt = u + u2
+ uuxxxx + µuxxtt + uxuxxx + u2
where , , , and µ are arbitrary constants. This equation may be thought of as a
fourth order analogue of a generalization of the...
We study the time and temperature dependent correlation functions for an impenetrable Bose gas with Neumann or Dirichlet boundary conditions (x1, 0)
(x2, t) ±,T .
We derive the Fredholm determinant formulae for the correlation functions, by means
of the Bethe Ansatz. For the special case x1 = 0, we...