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Elliptic and Complex Hypergeometric Integrals in Quantum Field Theory
AbstractWe consider relations between elliptic hypergeometric integrals and complex hypergeometric functions. Taking exactly computable type I...
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Exact solutions of the Landau–Ginzburg–Higgs equation utilizing the Jacobi elliptic functions
The Landau–Ginzburg–Higgs equation is one of the significant evolution equation in physical phenomena. In this work, the exact solutions of this...
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On the Existence of Superposed and Superposed-type Real and Complex Elliptic Periodic Waves of KdV Equation
The KdV equation serves as a mathematical model for ion acoustic waves in a plasma, long internal waves in a density-stratified ocean, acoustic waves...
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Elliptic K3 surfaces at infinite complex structure and their refined Kulikov models
Motivated by the Swampland Distance and the Emergent String Conjecture of Quantum Gravity, we analyse the infinite distance degenerations in the...
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Twisted elliptic genera
We study the twisted elliptic genera of 2d (0 , 4) SCFTs associated with the BPS strings in the twisted circle compactification of 6d rank-one (1 , 0)...
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Complex Creation Operator and Planar Automorphic Functions
We provide a concrete characterization of the poly-analytic planar automorphic functions, a special class of non analytic planar automorphic...
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A Use of Elliptic Complex Numbers in Newtonian Gravity
In this study, we used the fact that unit circle for elliptic numbers is an ellipse to model motion of a planet around a star. For that purpose we...
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Jacobi Elliptic Functions
Topic of this chapter are the Jacobi elliptic functions sn, cn, dn, their first derivatives, the additional nine Jacobi elliptic functions, and the...
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Elliptic Curves
Up to now we discussed mainly Feynman integrals, which can expressed in terms of multiple polylogarithms. Multiple polylogarithms are an important...
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Exact solutions for the improved mKdv equation with conformable derivative by using the Jacobi elliptic function expansion method
The goal of this paper is to find exact solutions to the improved modified Korteweg-de Vries (mKdV) equation with a conformable derivative using the...
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Modeling the complexity of elliptic black hole solution in 4D using Hamiltonian Monte Carlo with stacked neural networks
In this paper, we study the black hole solution of self-similar gravitational collapse in the Einstein-axion-dilaton system for the elliptic class in...
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An elliptic integrable deformation of the Principal Chiral Model
We introduce a new elliptic integrable σ -model in the form of a two-parameter deformation of the Principal Chiral Model on the group SL ℝ ( N ),...
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Elliptic families of solutions of the constrained Toda hierarchy
AbstractWe study elliptic families of solutions of the recently introduced constrained Toda hierarchy, i.e., solutions that are elliptic...
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An elliptic one-loop amplitude in anti-de-Sitter space
We present full analytic results for the four-point one-loop amplitude of a conformally coupled scalar in four-dimensional Anti-de-Sitter space dual...
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Hodge-Elliptic Genera, K3 Surfaces and Enumerative Geometry
K3 surfaces play a prominent role in string theory and algebraic geometry. The properties of their enumerative invariants have important consequences...
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New exact solution forms and stability aspects to Drinfel’d–Sokolov–Wilson model by using extended Jacobi elliptic rational function approach
In this study, the travelling wave solutions of the general Drinfel’d–Sokolov–Wilson (DSW)-system, introduced as a model of water waves, are obtained...
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Construction of chirped propagation with Jacobi elliptic functions for the nonlinear Schrödinger equations with quadratic nonlinearity with inter-modal and spatio-temporal dispersions
At the end of the past century, a completely new sort of soliton was discovered: embedded solitons. They were discovered in optical systems first,...
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Two off-axis elliptic optical vortices generated by an elliptic spiral forked plate
An elliptic spiral forked plate (ESFP) is proposed to generate two off-axis elliptic optical vortices, whose topological charges are identified by...
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An algorithmic approach to finding canonical differential equations for elliptic Feynman integrals
In recent years, differential equations have become the method of choice to compute multi-loop Feynman integrals. Whenever they can be cast into...