## 69 Citations

Abelian Functions for Purely Trigonal Curves of Genus Three

- Mathematics
- 2006

We develop the theory of generalized Weierstrass $\sigma$ and $\wp$ functions defined on a trigonal curve of genus three. The specific example of the `` purely trigonal\rq\rq curve $y^3=x^4+\lambda_3…

Identities for hyperelliptic ℘-functions of genus one, two and three in covariant form

- Mathematics
- 2008

We give a covariant treatment of the quadratic differential identities satisfied by the ℘-functions on the Jacobian of smooth hyperelliptic curves of genus ⩽3.

p-ADIC DIFFERENCE-DIFFERENCE LOTKA-VOLTERRA EQUATION AND ULTRA-DISCRETE LIMIT

- Mathematics
- 1999

We study the difference-difference Lotka-Volterra equations in p-adic number space and its p-adic valuation version. We point out that the structure of the space given by taking the ultra-discrete…

Abelian Functions for Trigonal Curves of Genus Three

- Mathematics
- 2010

We develop the theory of generalized Weierstrass sigma- and \wp-functions defined on a trigonal curve of genus three. In particular we give a list of the associated partial differential equations…

Toda Equations and σ-Functions of Genera One and Two

- Mathematics
- 2003

Abstract We study the Toda equations in the continuous level, discrete level and ultradiscrete level in terms of elliptic and hyperelliptic σ and ψ functions of genera one and two. The ultradiscrete…

Isogenies of certain K3 surfaces of rank 18

- MathematicsResearch in the Mathematical Sciences
- 2021

We construct geometric isogenies between three types of two-parameter families of K3 surfaces of Picard rank 18. One is the family of Kummer surfaces associated with Jacobians of genus-two curves…

Differential equations of genus four hyperelliptic ℘ functions

- Mathematics, BiologyJournal of Physics Communications
- 2021

It is shown that some differential equations are satisfied for general genus and the Hirota form is not enough to characterize the integrable differential equations.

Analytical and number-theoretical properties of the two-dimensional sigma function

- Mathematics
- 2020

This survey is devoted to the classical and modern problems related to the entire function ${\sigma({\bf u};\lambda)}$, defined by a family of nonsingular algebraic curves of genus $2$, where ${\bf…

Jacobi Inversion Formulae for a Curve in Weierstrass Normal Form

- MathematicsIntegrable Systems and Algebraic Geometry
- 2020

We consider a pointed curve $(X,P)$ which is given by the Weierstrass normal form, $y^r + A_{1}(x) y^{r-1} + A_{2}(x) y^{r-2} +\cdots + A_{r-1}(x) y+ A_{r}(x)$ where $x$ is an affine coordinate on…

Breather Turbulence: Exact Spectral and Stochastic Solutions of the Nonlinear Schrödinger Equation

- Environmental ScienceFluids
- 2019

I address the problem of breather turbulence in ocean waves from the point of view of the exact spectral solutions of the nonlinear Schrödinger (NLS) equation using two tools of mathematical physics:…