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The two (space)-dimensional generalisation of the Korteweg-de Vries (KdV) equation is the Kadomtsev-Petviashvili (KP) equation. This equation possesses two solitary wave type solutions. One is independent of the direction orthogonal to the direction of propagation and is the soliton solution of the KdV equation extended to two space dimensions. The other is a true two-dimensional solitary wave...
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