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Remarks on the generalized Kadomtsev-Petviashvili equations. (English) Zbl 0814.35119
The author studies the generalized KP equations \[ u_ t + u^ pu_ x + u_{xxx} + \varepsilon v_{y} = 0, \quad u_ y = v_ x. \] The aim is to investigate blow-up properties of solutions. The blow-up result concerns the case \(\varepsilon = - 1\) and \(p \geq 4\). The paper contains also results on local solvability.

MSC:
35Q53 KdV equations (Korteweg-de Vries equations)
35B40 Asymptotic behavior of solutions to PDEs
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