Darboux Transformation and Variable Separation Approach: the
Nizhnik-Novikov-Veselov Equation
HU Heng-Chun1, LOU Sen-Yue1,2, LIU Qing-Ping3
1Department of Physics, Shanghai Jiao Tong University, Shanghai 200030
2School of Mathematics, The University of New South Wales, Sydney, NSW 2052, Australia
3Beijing Graduate School, China University of Mining and Technology, Beijing 100083
Darboux Transformation and Variable Separation Approach: the
Nizhnik-Novikov-Veselov Equation
HU Heng-Chun1;LOU Sen-Yue1,2;LIU Qing-Ping3
1Department of Physics, Shanghai Jiao Tong University, Shanghai 200030
2School of Mathematics, The University of New South Wales, Sydney, NSW 2052, Australia
3Beijing Graduate School, China University of Mining and Technology, Beijing 100083
Abstract： Darboux transformation (DT) is developed to systematically find variable separation solutions for the Nizhnik-Novikov-Veselov equation. Starting from a seed solution with some arbitrary functions, the one-step DT yields the variable separable solutions, which can be obtained from the truncated Painlevé analysis, and the two-step DT 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.
2003, Vol. 20 
