Abstract
The three dimensional stability of nonlinear wave, soliton, and shock solutions of the nonlinear Schrodinger equation is examined. For the nonlinear waves the analysis is rigorous, whereas solitons are treated as limiting cases of the nonlinear waves. As two different limits yield the same result, this result is included. Shock solutions are again examined as limiting cases of the nonlinear waves, and for them an independent consideration of the limits at plus and minus infinity gives confirmation of the result. In contradistinction to the one dimensional analysis, which gave stability for some of the waves, the soliton and the shock, all these entities are now found to be unstable (though with varying degree of rigour in the treatment).
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