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  "body": "\n## Summary\n\nThe Kadomtsev–Petviashvili equation, or KP equation, is a nonlinear wave equation in two space variables $x$ and $y$.\nIt extends the [[Korteweg–De Vries equation|KTT75QC72Z]] to waves that move mainly in the $x$ direction but vary slowly in the $y$ direction.\nIt comes in two versions, KP-I and KP-II, which differ by the sign of the $u_{yy}$ term.\nLike the KdV equation it is completely integrable.\n\n## Explanations\n\n### L1 human\n\nThe KdV equation describes waves in a narrow canal, where the water moves along one line.\nOn a wide sea surface a wave crest is a long line, and it can bend a little.\nThe KP equation adds a small term that accounts for this sideways bending.\nEvery KdV wave that does not depend on $y$, such as a soliton with a straight crest, is also a KP wave.\nThe two sign choices model water with weak surface tension (KP-II) and with strong surface tension (KP-I).\n",
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