Abstract
The Bäcklund transformations for some nonlinear evolution equations (the Liouville, the sine and sinh-Poisson equations) are constructed through the AKNS system in unified manner. The obtained Bäcklund transformations are used to generate new classes of solutions. The latter is employed to obtain an infinite sequence of solutions. Moreover, we generate an infinite sequence of additional solutions by employing the permutability theorem and give a general expression for the
nth order solution. It turns out that this general expression can be employed to obtain solutions for the sine and sinh-Poisson equations. The final results are used to investigate some models in solar plasma physics. Conclusions and comments are given.