This research demonstrates quasi-periodic solutions in the mKdV equation using algebraic geometry methods, indicating advances in mathematical physics.
In the present paper, a hierarchy of the mKdV equation is integrated by the methods of algebraic geometry. The mKdV hierarchy in question arises on coadjoint orbits in the loop algebra of sl(2), and employs a family of hyperelliptic curves as spectral curves. A generic form of the finite-gap solution in any genus is obtained in terms of the -functions, which generalize the Weierstrass -function. Reality conditions for quasi-periodic wave solutions are completely specified. The obtained solutions are illustrated by plots in small genera.
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Julia Bernatska (2025) studied this question.
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