INTEGRABILITY CONDITIONS OF A STRUCTURE STATISFYING ƒ5 - a2ƒ= 0

AbstractWe investigate the integrability of Euler–Lagrange equations associated with 2D second-order Lagrangians of the form $$\begin{aligned} \int f(u_{xx},u_{xy},u_{yy})\ \mathrm{d}x\mathrm{d}y. \end{aligned}$$ ∫ f ( u xx , u xy , u yy ) d x d y . By deriving integrability conditions for the Lagrangian density f, examples of integrable Lagrangians expressible via elementary functions, Jacobi theta functions and dilogarithms are constructed. A link of second-order integrable Lagrangians to WDVV equations is established. Generalisations to 3D second-order integrable Lagrangians are also discussed.

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GEOMETRICAL CONSTRAINTS FOR D = 10, N = 1 SUPERGRAVITY

International Journal of Modern Physics A ◽

10.1142/s0217751x89001540 ◽

1989 ◽

Vol 04 (15) ◽

pp. 3819-3831 ◽

Cited By ~ 4

Author(s):

LING-LIE CHAU ◽

CHONG-SA LIM

Keyword(s):

Equations Of Motion ◽

Bianchi Identities ◽

Dynamical Consequence ◽

Integrability Conditions ◽

Geometrical Constraints ◽

Additional Constraints

A set of geometrical constraints for D = 10, N = 1 supergravity is formulated. It has the meaning as integrability conditions on "hyperplanes" determined by light-like lines in the superspace. The dynamical consequence of these geometrical constraints is studied via Bianchi identities. Since no equations of motion have resulted, these geometrical constraints can form an off-shell set of constraints for the theory. We also discuss additional constraints that lead to Poincare supergravity equations of motion. The relation of the theory with D = 4 N = 4 supergravity is also illuminated.

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Integrability Conditions: Recent Results in the Theory of Integrable Models

Differential Geometric Methods in Theoretical Physics - NATO ASI Series ◽

10.1007/978-1-4684-9148-7_6 ◽

1990 ◽

pp. 47-69

Author(s):

R. K. Bullough ◽

S. Olafsson ◽

Yu-Zhong Chen ◽

J. Timonen

Keyword(s):

Integrable Models ◽

Integrability Conditions

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On the spectrum and the distribution of singular values of Schrödinger operators with a complex potential

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1983.0078 ◽

1983 ◽

Vol 388 (1794) ◽

pp. 195-218 ◽

Cited By ~ 3

Keyword(s):

Complex Potential ◽

Spectral Properties ◽

Polynomial Growth ◽

Schrödinger Operators ◽

Singular Values ◽

Negative Real Part ◽

Adjoint Problem ◽

Schrodinger Operators ◽

Asymptotic Estimates ◽

Integrability Conditions

This paper is concerned with spectral properties of the Schrödinger operator ─ ∆+ q with a complex potential q which has non-negative real part and satisfies weak integrability conditions. The problem is dealt with as a genuine non-self-adjoint problem, not as a perturbation of a self-adjoint one, and global and asymptotic estimates are obtained for the corresponding singular values. From these estimates information is obtained about the eigenvalues of the problem. By way of illustration, detailed calculations are given for an example in which the potential has at most polynomial growth.

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