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This analysis demonstrates periodic solutions for the semi-discrete KP equation, suggesting connections to soliton solutions.
In this paper, we study the integrability and solution structure of the semi-discrete KP equation. We derive the bilinear Bäcklund transformation, Lax pair, and the nonlinear superposition formula of the semi-discrete KP equation. Periodic solutions are constructed by using Hirota’s method and Riemann theta functions. The asymptotic behavior of periodic solutions is analyzed and the connection between periodic solutions and soliton solutions is established.
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Li et al. (2025) studied this question.
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