In the framework of the theory of approximate transformation groups proposed by
Baikov, Gaziziv and Ibragimov , the first-order approximate symmetry operator is
calculated for the Navier-Stokes equations. The symmetries of the coupled system
obtained by expanding the dependent variables of the...
Effects of geometric constraints on a steady flow potential are described by an elliptic-
hyperbolic generalization of the harmonic map equations. Sufficient conditions are
given for global triviality.
The dependence on time of the moments of the one-soliton KdV solutions is given by
Bernoulli polynomials. Namely, we prove the formula
(x âˆ’ t) dx = 2 Ï€
Bn ( 1
Ï€ i) ,
expressing the moments of the one-soliton function sech
By computing certain cohomology of Vect(M ) of smooth vector fields we prove that
on 1-dimensional manifolds M there is no quantization map intertwining the action
of non-pro jective embeddings of the Lie algebra sl(2) into the Lie algebra Vect(M ).
Contrariwise, for pro jective embeddings sl(2)-equivariant...
In the framework of a multidimensional superposition principle involving an analytical
approach to nonlinear PDEs, a numerical technique for the analysis of soliton invari-
ant manifolds is developed. This experimental methodology is based on the use of
computer simulation data of solitonâ€“perturbation...
In this paper, based on the B âˆšÃ‰âˆšâ€ acklund transformation for the supersymmetric MKdV
equation, we propose a supersymmetric analogy for the second modified KdV equation.
We also calculate its one-, two- and three-soliton solutions.
The chain of discrete transformation equations is resolved in explicit form. The new
found form of solution alow to solve the problem of interrupting of the chain in the most
strigtforward way. More other this form of solution give a guess to its generalization on
the case of arbitrary semisimple...
The q-discrete two-dimensional Toda lattice equation with self-consistent sources is
presented through the source generalization procedure. In addition, the Gramm-
type determinant solutions of the system are obtained. Besides, a bilinear B Ìˆacklund
transformation (BT) for the system is given....
Rota-Baxter operators or relations were introduced to solve certain analytic and com-
binatorial problems and then applied to many fields in mathematics and mathematical
physics. In this paper, we commence to study the Rota-Baxter operators of weight
zero on pre-Lie algebras. Such operators satisfy...
The concept and use of recursion operators is well-established in the study of evolution, in
particular nonlinear, equations. We demonstrate the application of the idea of recursion
operators to ordinary differential equations. For the purposes of our demonstration we use
two equations, one chosen...