Zhixiong, Chen et al., Auto-Bäcklund Transformation and Analytic Solutions in One Dimensional Carrier Flow Equations, Acta Mathematica Sinica, New Series Chinese Journal of Mathematics, 9(4), 1993, pp. 438-445
We consider the simplifted one dimensional PDE's governing the carrier flow in semi-conductor devices via the Painlevé analysis approach, and obtain analytic solutions.