相关论文: Evaluations of Series Related to Jacobi Elliptic F…
By using some tools of analysis, we establish some analytical properties such as monotonicity and inequalities involving the hyperbolic sine integral function. As applications of some of the established properties, we obtain some rational…
We study conjugacy classes of solutions to systems of equations and inequations over torsion-free hyperbolic groups, and describe an algorithm to recognize whether or not there are finitely many conjugacy classes of solutions to such a…
Properties of solutions of generic hyperbolic systems with multiple characteristics with diagonalizable principal part are investigated. Solutions are represented as a Picard series with terms in the form of iterated Fourier integral…
In this paper, we consider systems of semilinear elliptic equations \displaystyle -\Delta_{\mathbb{H}^{N}}u=|v|^{p-1}v, \displaystyle -\Delta_{\mathbb{H}^{N}}v=|u|^{q-1}u, in the whole of Hyperbolic space $\mathbb{H}^{N}$. We establish…
Properties of four quintic theta functions are developed in parallel with those of the classical Jacobi null theta functions. The quintic theta functions are shown to satisfy analogues of Jacobi's quartic theta function identity and…
A definition of hyperbolic meromorphic functions is given and then we discuss the dynamical behavior and the thermodynamic formalism of hyperbolic functions on the Julia set. We prove the important expanding properties for hyperbolic…
In this paper we consider the linear second order partial differential equation with non-constant coefficients; then by using the double convolution product we produce new equations with polynomials coefficients and we classify the new…
The existence of hyperbolic orbits is proved for a class of singular Hamiltonian systems with repulsive potentials by taking limit for a sequence of periodic solutions which are the minimizers of variational functional
We evaluate several classes of high weight hypergeometric series via Gamma, polylogarithm and elliptic integrals, mainly through distribution relations.
We review the current status of one dimensional periodic potentials and also present several new results. It is shown that using the formalism of supersymmetric quantum mechanics, one can considerably enlarge the limited class of…
The parabolic trigonometric functions have recently been introduced as an intermediate step between circular and hyperbolic functions. They have been shown to be expressible in terms of irrational functions, linked to the solution of third…
In this note we consider functions with Moebius-periodic rational coefficients. These functions under some conditions take algebraic values and can be recovered by theta functions and the Dedekind eta function. Special cases are the…
A class of exact solutions of the Skyrme model are obtained. They are described by the Weierstrass $\wp$-function or the Jacobi elliptic function. They are not solitonic but of wave character. They supply us with examples of the…
The main purpose of this paper is to introduce moduli of smoothness with Jacobi weights $(1-x)^\alpha(1+x)^\beta$ for functions in the Jacobi weighted $L_p[-1,1]$, $0<p\le \infty$, spaces. These moduli are used to characterize the…
The geometric formulation of Hamilton--Jacobi theory for systems with nonholonomic constraints is developed, following the ideas of the authors in previous papers. The relation between the solutions of the Hamilton--Jacobi problem with the…
This paper is a contribution to the study of the relations between special functions, Lie algebras and rigged Hilbert spaces. The discrete indices and continuous variables of special functions are in correspondence with the representations…
This is an extended (factor 2.5) version of arXiv:math/0601371 and arXiv:0808.3486. We present new results in the theory of the classical $\theta$-functions of Jacobi: series expansions and defining ordinary differential equations (\odes).…
For a five-parameter discrete $\phi^4$ model, we derive various exact static solutions, including the staggered ones, in the form of the basic Jacobi elliptic functions $\sn$, $\cn$, and $\dn$, and also in the form of their hyperbolic…
In this paper, we point out that many Jacobi elliptic function solutions to non-linear differential equation(NDE) can be transformed each other via the modulus and phase transformation of Jacobi elliptic function. Therefore these solutions…
In this paper, we give a survey of a geometrical theory of Jacobi forms of higher degree. And we present some geometric results and discuss some geometric problems to be investigated in the future.