Elliptic (N,N^\prime)-Soliton Solutions of the lattice KP Equation

Abstract

Elliptic soliton solutions, i.e., a hierarchy of functions based on an elliptic seed solution, are constructed using an elliptic Cauchy kernel, for integrable lattice equations of Kadomtsev-Petviashvili (KP) type. This comprises the lattice KP, modified KP (mKP) and Schwarzian KP (SKP) equations as well as Hirota's bilinear KP equation, and their successive continuum limits. The reduction to the elliptic soliton solutions of KdV type lattice equations is also discussed.

18 pages

References in corpus (5)

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Cited by in corpus (2)

• Elliptic soliton solutions: $\tau$ functions, vertex operators and bilinear identities
• On the lattice-geometry and birational group of the six-point multi-ratio equation