Integrals of the Elliptic Integrals

Byrd, Paul F.; Friedman, Morris D.

doi:10.1007/978-3-642-52803-3_11

Cited by 48 publications

(83 citation statements)

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“…yei -63 v e ie 3 6 Throught the rest of the paper we will make use of elliptic functions as well as of other special functions following the conventions of [50,51,52].…”

Section: Distributions Of M2-branesmentioning

confidence: 99%

Domain walls of gauged supergravity, M-branes, and algebraic curves

Bakas¹,

Brandhuber²,

Sfetsos³

1999

Advances in Theoretical and Mathematical Physics

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We provide an algebraic classification of all supersymmetric domain wall solutions of maximal gauged supergravity in four and seven dimensions, in the presence of non-trivial scalar e-print archive: http://xxx.lanl.gov/hep-th/9912132 1658 I. BAKAS, A. BRANDHUBER, AND K. SFETSOS fields in the coset SL(8,R)/ SO(8) and SL(5,R)/SO(b) respectively. These solutions satisfy first-order equations, which can be obtained using the method of Bogomol'nyi. Prom an elevendimensional point of view they correspond to various continuous distributions of M2-and M5-branes. The Christoffel-Schwarz transformation and the uniformization of the associated algebraic curves are used in order to determine the Schrodinger potential for the scalar and graviton fluctuations on the corresponding backgrounds. In many cases we explicitly solve the Schrodinger problem by employing techniques of supersymmetric quantum mechanics. The analysis is parallel to the construction of domain walls of five-dimensional gauged supergravity, with scalar fields in the coset S , L(6,R)/5 , 0(6), using algebraic curves or continuous distributions of D3-branes in ten dimensions. In seven dimensions, in particular, our classification of domain walls is complete for the full scalar sector of gauged supergravity. We also discuss some general aspects of D-dimensional gravity coupled to scalar fields in the coset SL(N,R)/SO(N).

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“…yei -63 v e ie 3 6 Throught the rest of the paper we will make use of elliptic functions as well as of other special functions following the conventions of [50,51,52].…”

Section: Distributions Of M2-branesmentioning

confidence: 99%

Domain walls of gauged supergravity, M-branes, and algebraic curves

Bakas¹,

Brandhuber²,

Sfetsos³

1999

Advances in Theoretical and Mathematical Physics

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“…The data necessary to construct q will be expressed in terms of elliptic integrals and algebraic functions of the branch points. For these calculations, we rely heavily on the treatise by Byrd and Friedman [4]; citations of the form "formula xxx.yy" refer to this volume.…”

Section: Genus One Solutionsmentioning

confidence: 99%

“…(In equations (1), (3) and (4), and elsewhere in this paper, our conventions have been chosen so as to be consistent with the important monograph by Belokolos, Bobenko et al [1].) Because the first equation of (4) can be written as Lψ = λψ for a first-order matrix differential operator L, ψ is known as an eigenfunction associated with q.…”

Section: Introductionmentioning

confidence: 99%

Finite-Gap Solutions of the Vortex Filament Equation: Genus One Solutions and Symmetric Solutions

Calini

Ivey

2005

J Nonlinear Sci

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Abstract. For the class of quasi-periodic solutions of the vortex filament equation we study connections between the algebro-geometric data used for their explicit construction, and the geometry of the evolving curves. We give a complete description of genus one solutions, including geometrically interesting special cases such as Euler elastica, constant torsion curves, and self-intersecting filaments. We also prove generalizations of these connections to higher genus.

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“…The parameters α and A are now determined by requiring synchronization (11) and input datum (12), namely here by solving for unknowns α and A the system…”

Section: Bmentioning

confidence: 99%

“…The parameters β and A are determined as before by requiring synchronization (11) and input datum (12), namely…”

Section: Cmentioning

confidence: 99%

Bistability in the sine-Gordon equation: The ideal switch

Khomeriki

León

2005

Phys. Rev. E

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The sine-Gordon equation, used as the representative nonlinear wave equation, presents a bistable behavior resulting from nonlinearity and generating hysteresis properties. We show that the process can be understood in a comprehensive analytical formulation and that it is a generic property of nonlinear systems possessing a natural band gap. The approach allows to discover that sine-Gordon can work as an ideal switch by reaching a transmissive regime with vanishing driving amplitude.

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Integrals of the Elliptic Integrals

Cited by 48 publications

References 0 publications

Domain walls of gauged supergravity, M-branes, and algebraic curves

Domain walls of gauged supergravity, M-branes, and algebraic curves

Finite-Gap Solutions of the Vortex Filament Equation: Genus One Solutions and Symmetric Solutions

Bistability in the sine-Gordon equation: The ideal switch

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