Broadband electrostatic wave (BEN) data gathered from Polar for passes through the aurora are analyzed and compared with theoretical predictions for the origin of magnetized solitary waves in BEN. Two passes exhibiting solitary waves were chosen for comparison, and times were selected that show numerous such waves. Examination of the data shows that even for these cases the nonsolitary form of BEN occurs much more commonly than the solitary form that is being particularly examined here. The first pass was for the period of 1430--1550 UT on 7 April 1996 at distances near 7RE, and the second pass was for the period of 0600--0800 UT on 10 May 1996 at distances near 8.8 RE. Four short intervals were chosen from the passes that show interesting solitary waves, each at slightly different radial distance, and the plasma parameters measured are used in developed theory to give predictions for the minimum and maximum electric field for propagation of BGK solitary waves, which have been the focus of theory for the nonlinear form of BEN for over a decade. This predicted minimum is compared to observations for solitary waves observed in these spacecraft time intervals along with parameters of the plasma environment at the time of observation, identified from the HYDRA data for these passes. The actual electric field is found to lie below the predicted minimum for all cases. Our conclusion is that these solitary waves are clearly not BGK waves in their observed form and may possibly have been produced by means other than electron trapping processes for BGK solitary waves. Feasible alternative theories for the solitary waves are discussed.