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81.
The motion of a particle in the field of an electromagnetic monopole (in the Coulomb–Dirac field) perturbed by an axially symmetric potential after quantum averaging is described by an integrable system. Its Hamiltonian can be written in terms of the generators of an algebra with quadratic commutation relations. We construct the irreducible representations of this algebra in terms of second-order differential operators; we also construct its hypergeometric coherent states. We use these states in the first-order approximation with respect to the perturbing field to obtain the integral representation of the eigenfunctions of the original problem in terms of solutions of the model Heun-type second-order ordinary differential equation and present the asymptotic approximation of the corresponding eigenvalues. 相似文献
82.
We solve the problem of describing compatible nonlocal Poisson brackets of hydrodynamic type. We prove that for nonsingular pairs of compatible nonlocal Poisson brackets of hydrodynamic type, there exist special local coordinates such that the metrics and the Weingarten operators of both brackets are diagonal. The nonlinear evolution equations describing all nonsingular pairs of compatible nonlocal Poisson brackets of hydrodynamic type are derived in these special coordinates, and the integrability of these equations is proved using the inverse scattering transform. The Lax pairs with a spectral parameter for these equations are found. We construct various classes of integrable reductions of the derived equations. These classes of reductions are of an independent differential-geometric and applied interest. In particular, if one of the compatible Poisson brackets is local, we obtain integrable reductions of the classical Lamé equations describing all orthogonal curvilinear coordinate systems in a flat space; if one of the compatible brackets is generated by a constant-curvature metric, the corresponding equations describe integrable reductions of the equations for orthogonal curvilinear coordinate systems in a space of constant curvature. 相似文献
83.
84.
Dynamical behaviour and exact solutions of thirteenth order derivative nonlinear Schr\"{o}dinger equation 下载免费PDF全文
In this paper, we considered the model of the thirteenth order derivatives of nonlinear Schr\"{o}dinger equations. It is shown that a wave packet ansatz inserted into these equations leads to an integrable Hamiltonian dynamical sub-system. By using bifurcation theory of planar dynamical systems, in different parametric regions, we determined the phase portraits. In each of these parametric regions we obtain possible exact explicit parametric representation of the traveling wave solutions corresponding to homoclinic, hetroclinic and periodic orbits. 相似文献
85.
T. V. Skrypnyk 《Theoretical and Mathematical Physics》2008,155(1):633-645
Using the R-operator on a Lie algebra
satisfying the modified classical Yang-Baxter equation, we define two sets of functions that mutually commute with respect
to the initial Lie-Poisson bracket on
. We consider examples of the Lie algebras
with the Kostant-Adler-Symes and triangular decompositions, their R-operators, and the corresponding two sets of mutually
commuting functions in detail. We answer the question for which R-operators the constructed sets of functions also commute
with respect to the R-bracket. We briefly discuss the Euler-Arnold-type integrable equations for which the constructed commutative
functions constitute the algebra of first integrals.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 155, No. 1, pp. 147–160, April, 2008. 相似文献
86.
一类广义Riccati方程的三个可积判据 总被引:1,自引:1,他引:1
考虑一类广义Riccati方程,通过函数变换,在所给条件下,将这类方程等价地化为变量分离方程,从而得到了该方程可积的三个充分性判据,并给出方程通解的参数表达形式,扩大了Riccati方程的可解性范围. 相似文献
87.
88.
We derive bosonic-type formulas for the characters of
2 coinvariants. 相似文献
89.
O. I. Mokhov 《Theoretical and Mathematical Physics》2002,133(2):1557-1564
We prove that two Dubrovin–Novikov Hamiltonian operators are compatible if and only if one of these operators is the Lie derivative of the other operator along a certain vector field. We consider the class of flat manifolds, which correspond to arbitrary pairs of compatible Dubrovin–Novikov Hamiltonian operators. Locally, these manifolds are defined by solutions of a system of nonlinear equations, which is integrable by the method of the inverse scattering problem. We construct the integrable hierarchies generated by arbitrary pairs of compatible Dubrovin–Novikov Hamiltonian operators. 相似文献
90.
We discuss the relationship between the representation of an integrable system as an L-A-pair with a spectral parameter and the existence of two compatible Hamiltonian representations of this system. We consider examples of compatible Poisson brackets on Lie algebras, as well as the corresponding integrable Hamiltonian systems and Lax representations. 相似文献