36 citations · 248 across the 57 of their papers we have counts for
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Trigonal Toda lattice Equation
Shigeki Matsutani
In this article, we give the trigonal Toda lattice equation, $$ -\frac{1}{2}\frac{d^3}{d t^3} q_{\ell}(t) = e^{q_{\ell+1}(t)} +e^{q_{\ell+ζ_3}(t)} +e^{q_{\ell+ζ_3^2}(t)}-3e^{q_\ell…
Relations of al Functions over Subvarieties in a Hyperelliptic Jacobian
Shigeki Matsutani
The sine-Gordon equation has hyperelliptic al function solutions over a hyperelliptic Jacobian for of arbitrary genus . This article gives an extension of the sine-…
On Relations of Hyperelliptic Weierstrass al Functions
Shigeki Matsutani
We study relations of the Weierstrass's hyperelliptic al-functions over a non-degenerated hyperelliptic curve of arbitrary genus as solutions of sine-Gordon equati…
Hyperelliptic Solutions of Modified Korteweg-de Vries Equation of Genus g: Essentials of Miura Transformation
Shigeki Matsutani
Explicit hyperelliptic solutions of the modified Korteweg-de Vries equations without any ambiguous parameters were constructed in terms only of the hyperelliptic $\al$-functions ov…
Hyperelliptic Loop Solitons with Genus g: Investigations of a Quantized Elastica
Shigeki Matsutani
In the previous work (J. Geom. Phys. {\bf{39}} (2001) 50-61), the closed loop solitons in a plane, \it i.e., loops whose curvatures obey the modified Korteweg-de Vries equations, w…
Hyperelliptic Solutions of KdV and KP equations: Reevaluation of Baker's Study on Hyperelliptic Sigma Functions
Shigeki Matsutani
Explicit function forms of hyperelliptic solutions of Korteweg-de Vries (KdV) and \break Kadomtsev-Petviashvili (KP) equations were constructed for a given curve whose…