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