Elliptic soliton solutions, comprising a soliton-type hierarchy of functions based on an elliptic seed solution, are constructed using elliptic Cauchy matrices, for a family of integrable lattice equations of Kadomtsev-Petviashvili (KP) type. This family consists of the lattice KP, modified KP, and Schwarzian KP 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.
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American Institute of Physics
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