Abstract
Recently, considerable progress has been made in understanding the nature of the algebro-geometrical superposition principles for the solutions of nonlinear completely integrable evolution equations, and mainly for the equations related to hyperelliptic Riemann surfaces. Here we find such a superposition formula for particular real solutions of the KP and Boussinesq equations related to the nonhyperelliptic curve ω4 = (λ − E 1) (λ − E 2) (λ − E 3) (λ − E 4). It is shown that the associated Riemann theta function may be decomposed into a sum containing two terms, each term being the product of three one-dimensional theta functions. The space and time variables of the KP and Boussinesq equations enter into the arguments of these one-dimensional theta functions in a linear way.
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On leave from Leningrad State University and Leningrad Institute of Aviation Instrumentation.
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Matveev, V.B., Smirnov, A.O. On the Riemann theta function of a trigonal curve and solutions of the Boussinesq and KP equations. Lett Math Phys 14, 25–31 (1987). https://doi.org/10.1007/BF00403466
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DOI: https://doi.org/10.1007/BF00403466