Bäcklund transformations and exact solutions for some nonlinear evolution equations in solar magnetostatic models

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...

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Published in:Journal of computational and applied mathematics 2002-03, Vol.140 (1), p.435-467
Main Authors: Khater, A.H., Callebaut, D.K., Malfliet, W., Kamel, E.S.
Format: Article
Language:English
Subjects:
Astronomy
Bäcklund transformations
Earth, ocean, space
Electric and magnetic fields
Exact sciences and technology
Exact solutions
Nonlinear evolution equations
Solar magnetohydrodynamics
Solar physics
Solar system
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description 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.
doi_str_mv 10.1016/S0377-0427(01)00481-2
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source ScienceDirect Freedom Collection 2022-2024
subjects Astronomy
Bäcklund transformations
Earth, ocean, space
Electric and magnetic fields
Exact sciences and technology
Exact solutions
Nonlinear evolution equations
Solar magnetohydrodynamics
Solar physics
Solar system
title Bäcklund transformations and exact solutions for some nonlinear evolution equations in solar magnetostatic models
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