Abstract
A modified Kadomtsev–Petviashvili (MKP) equation is proposed. The equation is a weakly two-dimensional generalisation of the Schamel equation. It is shown that one form of this equation arises in the context of the propagation of ion-acoustic waves in a plasma with non-isothermal electrons. The stability of certain plane periodic and solitary travelling wave solutions of the MKP equation to two-dimensional long wavelength perturbations is investigated using the method of Rowlands and Infeld. The results obtained are compared with those for the standard KP equation; some qualitative differences are found.
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