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Bäcklund Transformations and Exact Solutions for Some Nonlinear Evolution Equations in Solar Magnetostatic Models.

Author name : Eid Sayed K Sayed
Publication Date : 2002-03-10
Journal Name : Journal Of Computational And Applied Mathematics

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.

Keywords

Solar magnetohydrodynamics , Bäcklund transformations , Nonlinear evolution equations, Exact solutions

Publication Link

https://doi.org/10.1016/S0377-0427(01)00481-2

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