On real hyperelliptic solutions of focusing modified KdV equation

2023/09/10 by Shigeki Matsutani, Matsutani, Shigeki · 3 citations
Physics and Astronomy · Mathematics · #Nonlinear Waves and Solitons #Black Holes and Theoretical Physics #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2309.04904

Abstract

We study the real hyperelliptic solutions of the focusing modified KdV (MKdV) equation of the genus three. Since the complex hyperelliptic solutions of the focusing MKdV equation over ℂ are associated with the real gauged MKdV equation, we present a novel construction of the real hyperelliptic solutions of the gauged MKdV equation. When the gauge field is constant, it can be regarded as the real solution of the focusing MKdV equation, and thus we also discuss the behavior of the gauge field numerically.

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• Exact quasi-periodic solutions to the MKdV equation
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