Related papers: On a classical solution to the Abelian Higgs model
We derive equations of motion for poles of elliptic solutions to the B-version of the Kadomtsev-Petviashvili equation (BKP). The basic tool is the auxiliary linear problem for the Baker-Akhiezer function. We also discuss integrals of motion…
In this article we solve a class of two parameter polynomial-quintic equation. The solution follows if we consider the Jacobian elliptic function $sn$ and relate it with the coefficients of the equation. The solution is the elliptic…
A generalization of Jacobi's elliptic functions is introduced as inversions of hyperelliptic integrals. We discuss the special properties of these functions, present addition theorems and give a list of indefinite integrals. As a physical…
We give a new method to prove in a uniform and easy way various transformation formulas for Gauss hypergeometric functions. The key is Jacobi's canonical form of the hypergeometric differential equation. Analogy for $q$-hypergeometric…
We develop the theory of Abelian functions associated with algebraic curves. The growth in computer power and an advancement of efficient symbolic computation techniques has allowed for recent progress in this area. In this paper we focus…
We introduce the notion of abelian solutions of KP equations and show that all of them are algebro-geometric.
The problem of the motion of a particle in an asymmetric double well is solved explicitly in terms of the Weierstrass and Jacobi elliptic functions. While the solution of the orbital motion is expressed simply in terms of the Weierstrass…
Exact solutions are found for Euler's equations of rigid body motion for general asymmetrical bodies under the influence of torque by using Jacobi elliptic functions. Differential equations are determined for the amplitudes and the…
A Lagrangian description of a classical particle in a 9-dimensional flat Finslerian space with a cubic metric function is constructed. The general solution of equations of motion for such a particle is obtained. The Galilean law of inertia…
The nature of the Abelian Higgs Model phase transition is investigated. A variational approximation is used in the evaluation of the relevant finite temperature effective potential. Some of the results presented are valid not only in the…
The description of many dynamical problems like the particle motion in higher dimensional spherically and axially symmetric space-times is reduced to the inversion of a holomorphic hyperelliptic integral. The result of the inversion is…
All real solutions of the Lane-Emden equation for n = 5 are obtained in terms of Jacobian and Weierstrass elliptic functions. A new family of solutions is found. It is expressed by remarkably simple formulae involving Jacobian elliptic…
The Jacobi and Weierstrass elliptic functions used to be part of the standard mathematical arsenal of physics students. They appear as solutions of many important problems in classical mechanics: the motion of a planar pendulum (Jacobi),…
We develop the theory of Abelian functions associated with cyclic trigonal curves by considering two new cases. We investigate curves of genus six and seven and consider whether it is the trigonal nature or the genus which dictates certain…
We study Heun's differential equation in the case that one of the singularities is apparent. In particular we conjecture a relationship with generalized hypergeometric differential equation and establish it in some cases. We apply our…
General analytical solutions of the Quantum Hamilton Jacobi Equation for conservative one-dimensional or reducible motion are presented and discussed. The quantum Hamilton's characteristic function and its derivative, i.e. the quantum…
In a recent paper, the canonical forms of a new multi-parameter class of Abel differential equations, so-called AIR, all of whose members can be mapped into Riccati equations, were shown to be related to the differential equations for the…
We investigate the Non-Commutative Abelian Higgs model. We argue that it is possible to introduce a consistent renormalization method by imposing the Non-commutative BRST invariance of the theory and by introducing the Non-Commutative…
In this article we give evaluations of certain series of hyperbolic functions using Jacobi elliptic functions theory. We also define some new functions that enable us to give characterization of not solvable class of series.
The description of many dynamical problems like the particle motion in higher dimensional spherically and axially symmetric space-times is reduced to the inversion of hyperelliptic integrals of all three kinds. The result of the inversion…