On Relations of Hyperelliptic Weierstrass al Functions
Shigeki Matsutani
Abstract
We study relations of the Weierstrass's hyperelliptic al-functions over a non-degenerated hyperelliptic curve y2 = f(x) of arbitrary genus g as solutions of sine-Gordon equation using Weierstrass's local parameters, which are characterized by two ramified points. Though the hyperelliptic solutions of the sine-Gordon equation had already obtained, our derivations of them are simple; they need only residual computations over the curve and primitive matrix computations.
Create a lesson
Related papers
Integrability of the deformed Toda systems
Mikhail Vasilev
An integrable Z22-graded extension of Camassa-Holm equation and its bi-Hamiltonian structure
N. Aizawa, Ichi Fujii, Ren Ito et al.
Maxwell's relations as Hamilton's equations: a symplectic and variational framework
Sikarin Yoo-Kong
The Nakamura Conjecture Revisited: Toda Molecules and Stationary Axisymmetric Gravity
Takeshi Fukuyama
Multivariable Painleve'-II equation: connection formulas for arbitrary system size
Nikolai A. Sinitsyn
Vector rogue wave patterns associated with generalized Hermite and Okamoto polynomials
Hejiaqi Chen, Dongwei Wu, Chengfa Wu et al.