are however three famous cases that are integrable, the Euler, the Lagrange, and the Kovalevskaya top, which are in fact the only integrable cases when...

that is "completely integrable" other than the tops of Euler and Lagrange. In 1889 Kovalevskaya was appointed Ordinary Professor (full professor) at Stockholm...

ForeverSpin Jacks are spun as tops upon one of their points or used to play knucklebones Lagrange, Euler, and Kovalevskaya tops Paengi Chigi Yo-yo Cromwell...

Korteweg–de Vries equation Sine-Gordon equation Toda lattice Lagrange, Euler, and Kovalevskaya tops Belinski–Zakharov transform, in general relativity. The...

{\displaystyle (H,\mathbf {L} ^{2},L_{3})} . Integrable tops: The Lagrange, Euler and Kovalevskaya tops are integrable in the Liouville sense. Frobenius integrability:...

ellipsoids Harmonic oscillator Integrable Clebsch and Steklov systems in fluids Lagrange, Euler, and Kovalevskaya tops Neumann oscillator Two center Newtonian gravitational...

}{\partial x}}.} Derivation of Euler–Lagrange equations Since the Lagrangian (eq (1)) contains second derivatives, the Euler–Lagrange equation of motion for this...

is a statistical mechanical model used in the study of critical points and phase transitions of magnetic systems, in which the spins of the magnetic...

\varphi _{tt}-\varphi _{xx}+\varphi =0.} The sine-Gordon equation is the Euler–Lagrange equation of the field whose Lagrangian density is given by L SG ( φ...

four) famous cases that are integrable, the Euler, the Lagrange, and the Kovalevskaya top. The Kovalevskaya top is a special symmetric top with a unique...

responsible for wave scattering.: 66–67  The direct and inverse scattering transforms are analogous to the direct and inverse Fourier transforms which are used...

rediscovered and studied by Kevin Costello, and later by Edward Witten and Masahito Yamazaki. It is named after mathematicians Shiing-Shen Chern and James Simons...

Takhtajan and L. D. Faddeev in 1979. It can be viewed as a quantized version of the classical inverse scattering method pioneered by Norman Zabusky and Martin...

G_{L}\times G_{R}} , the left and right copies, respectively; where the left copy acts as the left action upon the target space, and the right copy acts as the...

and a compact Riemann surface, introduced by Nigel Hitchin in 1987. It lies on the crossroads of algebraic geometry, the theory of Lie algebras and integrable...

the algebraic curve that the theory is defined on is the Riemann sphere and the system is tamely ramified. The Schlesinger equations are a system of...