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Riemann Surfaces and Theta Functions
FiniteGap Solutions of the KadomtsevPetviashvili
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Abelian differentials Abelian integrals algebraic curve algebro-geometric arbitrary asymptotic automorphism Baker-Akhiezer function basis of cycles boundary branch points characteristics coefficients consider constructed corresponding curve Xg defined denote derive described divisor domain F electron elliptic functions equal equivalent expression finite finite-gap potentials finite-gap solutions fixed points formulas Fuchsian group fundamental domain gaps genus g given group G Hamiltonian holomorphic differentials homology basis hyperelliptic curve invariant inverse involution Jacobi KdV equation Kowalewski KP equation KP2 equation Krichever lattice Lax representation Lemma M-curve mapping Matveev meromorphic function neighborhood nonlinear normalized obtain parameters Peierls period matrix periodic potential poles polynomial potential u(x problem proof reduction relation respect Riemann surface Riemann theta functions Schottky group Schrodinger operator second kind Sect sine-Gordon equation single-valued singularities soliton spectrum Theorem theory theta constants torus transformation uniformization variable vector wave Weierstrass zero