Darboux Transformation and Variable Separation Approach: the   Nizhnik-Novikov-Veselov equation
  Darboux transformation is developed to systematically find variable separation solutions for the Nizhnik-Novikov-Veselov equation. Starting from a seed solution with some arbitrary functions, the once Darboux transformation yields the variable separable solutions which can be obtained from the truncated Painlev\'e analysis and the twice Darboux transformation leads to some new variable separable solutions which are the generalization of the known results obtained by using a guess ansatz to solve the generalized trilinear equation. 
Heng-chun Hu, Sen-yue Lou and Qing-ping Liu