Backlund transformations and exact soliton solutions for some nonlinear evolution equations of the ZS/AKNS system

The general form of the Backlund transformations (BTs) for some nonlinear e volution equations (NLEEs) solvable by the inverse scattering method of Zak harov-Shabat/Ablowitz- Kaup-Newell-Segur (ZS/AKNS) and the ZS/AKNS wave fun ctions corresponding to the soliton solutions of these NLEEs are considered . The method of characteristics is used and BTs are employed to generate ne w solutions from the old. Thus, families of new solution classes for the Kd V equation, the mKdV equation, the sinh-Poisson equation, the Liouville equ ation, the stable nonlinear Schrodinger equation, the unstable nonlinear Sc hrodinger equation, and the inhomogeneous nonlinear Schrodinger equation ar e obtained. (C) 1998 Elsevier Science Ltd. All rights reserved.