ISSN:1402-9251    

DOI:10.2991/jnmp.2000.7.3.6

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

So far, there are described in the literature two ways to superize the Liouville equation: for a scalar field (forN≤4) and for a vector-valued field (analogs of the Leznov – Saveliev equations) forN=1. Both superizations are performed with the help of Neveu–Schwarz superalgebra. We consider another version of these superLiouville equations based on the Ramond superalgebra, their explicit solutions are given by Ivanov–Krivonos’ scheme. Open problems are offered.

ISSN:1402-9251    

DOI:10.2991/jnmp.2000.7.3.1

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

In the homogenization of monotone parabolic partial differential equations with oscillations in both the space and time variables the gradients converges only weakly inLp. In the present paper we construct a family of correctors, such that, up to a remainder which converges to zero strongly inLp, we obtain strong convergence of the gradients inLp.

ISSN:1402-9251    

DOI:10.2991/jnmp.2000.7.3.2

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

We prove the existence of non-decaying real solutions of the Johnson equation, vanishing asx→+∞. We obtain asymptotic formulas ast→ ∞for the solutions in the form of an infinite series of asymptotic solitons with curved lines of constant phase and varying amplitude and width.

ISSN:1402-9251    

DOI:10.2991/jnmp.2000.7.3.3

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

SeveralN-body problems in ordinary (3-dimensional) space are introduced which are characterized by Newtonian equations of motion (“acceleration equal force;” in most cases, the forces are velocity-dependent) and are amenable to exact treatment (“solvable” and/or “integrable” and/or “linearizable”). These equations of motion are always rotation-invariant, and sometimes translation-invariant as well. In many cases they are Hamiltonian, but the discussion of this aspect is postponed to a subsequent paper. We consider “few-body problems” (with, say,N=1,2,3,4,6,8,12,16,...) as well as “many-body problems” (Nan arbitrary positive integer). The main focus of this paper is on various techniques to uncover suchN-body problems. We do not discuss the detailed behavior of the solutions of all these problems, but we do identify several models whose motions are completely periodic or multiply periodic, and we exhibit in rather explicit form the solutions in some cases.

ISSN:1402-9251    

DOI:10.2991/jnmp.2000.7.3.4

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

A toy top is defined as a rotationally symmetric body moving in a constant gravitational field while one point on the symmetry axis is constrained to stay in a horizontal plane. It is an integrable system similar to the Lagrange top. Euler-Poisson equations are derived. Following Felix Klein, the special unitary group SU(2) is used as configuration space and the solution is given in terms of hyperelliptic integrals. The curve traced by the point moving in the horizontal plane is analyzed, and a qualitative classification is achieved. The cases in which the hyperelliptic integrals degenerate to elliptic ones are found and the corresponding solutions are given in terms of Weierstrass elliptic functions.

ISSN:1402-9251    

DOI:10.2991/jnmp.2000.7.3.5

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor