7,051 research outputs found
Analytical description of the coherent structures within the hyperbolic generalization of Burgers equation
We present new periodic, kink-like and soliton-like travelling wave solutions
to the hyperbolic generalization of Burgers equation. To obtain them, we employ
the classical and generalized symmetry methods and the ansatz-based approachComment: 12 pages, 8 figure
Magnetohydrodynamic drift equations : from Langmuir circulations to magnetohydrodynamic dynamo?
We derive the closed system of averaged magnetohydrodynamic (MHD) equations for general oscillating flows. The used small parameter of our asymptotic theory is the dimensionless inverse frequency, and the leading term for a velocity field is chosen to be purely oscillating. The employed mathematical approach combines the two timing method and the notion of a distinguished limit. The properties of commutators are used to simplify calculations. The derived averaged equations are similar to the original MHD equations, but surprisingly (instead of the commonly expected Reynolds stresses) a drift velocity plays a part of an additional advection velocity. In the special case of a vanishing magnetic field , the averaged equations produce the Craik–Leibovich equations for Langmuir circulations (which can be called ‘vortex dynamo’). We suggest that, since the mathematical structure of the full averaged equations for is similar to those for , these full equations could lead to a possible mechanism of MHD dynamo, such as the generation of the magnetic field of the Earth
A Closed Expression for the Universal R-Matrix in a Non-Standard Quantum Double
In recent papers of the author, a method was developed for constructing
quasitriangular Hopf algebras (quantum groups) of the quantum-double type. As a
by-product, a novel non-standard example of the quantum double has been found.
In the present paper, a closed expression (in terms of elementary functions)
for the corresponding universal R-matrix is obtained. In reduced form, when the
number of generators becomes two instead of four, this quantum group can be
interpreted as a deformation of the Lie algebra
[x,h]=2h in the context of Drinfeld's quantization program.Comment: 6 pages, LATEX, JINR preprint E2-93-15
On the equation of the -adic open string for the scalar tachyon field
We study the structure of solutions of the one-dimensional non-linear
pseudodifferential equation describing the dynamics of the -adic open string
for the scalar tachyon field . We elicit
the role of real zeros of the entire function and the behaviour of
solutions in the neighbourhood of these zeros. We point out that
discontinuous solutions can appear if is even. We use the method of
expanding the solution and the function in the Hermite
polynomials and modified Hermite polynomials and establish a connection between
the coefficients of these expansions (integral conservation laws). For we
construct an infinite system of non-linear equations in the unknown Hermite
coefficients and study its structure. We consider the 3-approximation. We
indicate a connection between the problems stated and the non-linear
boundary-value problem for the heat equation.Comment: AMSTeX, 26 page
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