Bäcklund transformation and exact soliton solutions for some nonlinear evolution equations of the ZS/AKNS system
The Bäcklund transformations (BTs) technique is one of the direct methods to obtain the new soliton solutions of a given nonlinear evolution equations (NLEEs). The Bäcklund transformations explicitly express the new solutions in terms of the known solutions of the NLEEs and the corresponding wave functions which are solutions of the associated Zakharov-Shabat/Ablowitz-Kaup-Newell-Segur (ZS/AKNS) system. The main goal of this paper is to use BTs in the construction of exact soliton solutions for some classes of NLEEs, for instance: for KdV, mKdV, Liouville, stable and nonstable Schrödinger and many others. To this end the method of characteristics is used.
scientific article; zbMATH DE number 1371614