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On an elliptic extension of the Kadomtsev-Petviashvili equation

A generalisation of the Lattice Potential Kadomtsev-Petviashvili (LPKP) equation is presented, using the method of Direct Linearisation based on an elliptic Cauchy kernel. This yields a (3+1)-dimensional lattice system with one of the lattice shifts singled out. The integrability of the lattice system is considered, presenting a Lax representation and soliton solutions. An associated continuous system is also derived, yielding a (3+1)-dimensional generalisation of the potential KP equation associated with an elliptic curve.

preprint2013arXivOpen access
Paul JenningsFrank Nijhoff
nlin.SI
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Paul JenningsFrank Nijhoff

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