Darboux transformation of a nonlinear evolution equation and its explicit solutions

2011 ◽  
Vol 31 (4) ◽  
pp. 1457-1464 ◽  
Author(s):  
Li Wenmin ◽  
Han Youpan ◽  
Zhou Gaojun
Keyword(s):  
Evolution Equation ◽  
Darboux Transformation ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Evolution ◽  
Explicit Solutions

DARBOUX TRANSFORMATION AND VARIOUS SOLUTIONS FOR A NONLINEAR EVOLUTION EQUATION IN (3 + 1)-DIMENSIONS

2008 ◽  
Vol 22 (30) ◽  
pp. 2945-2966 ◽  
Author(s):  
ZHAQILAO ◽  
ZHI-BIN LI
Keyword(s):  
Evolution Equation ◽  
Soliton Solution ◽  
Darboux Transformation ◽  
Nonlinear Evolution Equation ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Spectral Problems ◽  
Complexiton Solution

A new (3 + 1)-dimensional nonlinear evolution equation can be decomposed into three (1 + 1)-dimensional nonlinear evolution equations. In this paper, N-soliton solution, resonant solution and complexiton solution of the (3 + 1)-dimensional nonlinear evolution equation are obtained via an N-fold Darboux transformation of the Ablowitz–Kaup–Newell–Segur spectral problems.

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