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A new, completely integrable, two dimensional evolution equation is derivedfor an ion acoustic wave propagating in a magnetized, collisionless plasma. Theequation is a multidimensional generalization of a modulated wavepacket withweak transverse propagation, which has resemblance to nonlinear Schrodinger(NLS) equation and has a connection to Kadomtsev-Petviashvili equation througha constraint relation. Higher soliton solutions of the equation are derivedthrough Hirota bili- nearization procedure, and an exact lump solution iscalculated exhibiting 2D structure. Some mathe- matical propertiesdemonstrating the completely integrable nature of this equation are described.Modulational instability using nonlinear frequency correction is derived, andthe corresponding growth rate is calculated, which shows the directionalasymmetry of the system. The discovery of this novel (2{\th}1) dimensionalintegrable NLS type equation for a magnetized plasma should pave a newdirection of research in the field.

A new (2+1) dimensional integrable evolution equation for an ion acoustic wave in a magnetized plasma