On Real Hyperelliptic Solutions of Focusing Modified KdV Equation

Matsutani, Shigeki

doi:10.1007/s11040-024-09490-z

Math Phys Anal Geom

2024

DOI: 10.1007/s11040-024-09490-z

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On Real Hyperelliptic Solutions of Focusing Modified KdV Equation

Shigeki Matsutani

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Cited by 2 publications

References 26 publications

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A numerical representation of hyperelliptic KdV solutions

Matsutani

2024

Communications in Nonlinear Science and Numerical Simulation

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A numerical representation of hyperelliptic KdV solutions

Matsutani

2024

Communications in Nonlinear Science and Numerical Simulation

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Nonlinear Schrödinger equation in terms of elliptic and hyperelliptic σ functions

Matsutani

2024

J. Phys. A: Math. Theor.

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It is known that the elliptic function solutions of the nonlinear Schrödinger equation are reduced to the algebraic diﬀerential relation in terms of the WeierWeierstrass sigma function, (-i∂/∂t‒ α ∂/∂u-(1/2) ∂2/ ∂u2)/Ψ + (Ψ∗Ψ)Ψ =(1/2)(2β + α2 − 3℘(v))Ψ, where Ψ(u;v, t) := exp(αu+iβt+c−ζ(v)u)σ(u + v)/σ(u)σ(v), its dual Ψ∗(u; v, t), and certain complexand certain complex numbers α, β and c. In this paper, we generalize the algebraic differential relation to those of genera two and three in terms of the hyperelliptic sigma functions.

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On Real Hyperelliptic Solutions of Focusing Modified KdV Equation

Cited by 2 publications

References 26 publications

A numerical representation of hyperelliptic KdV solutions

A numerical representation of hyperelliptic KdV solutions

Nonlinear Schrödinger equation in terms of elliptic and hyperelliptic σ functions

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