Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2011-11-22
Nonlinear Sciences
Exactly Solvable and Integrable Systems
18 pages
Scientific paper
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.
Nijhoff Frank
Yoo-Kong Sikarin
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