The inhomogeneous extension of equations of the reaction–diffusion type is investigated by means of the covariant prolongation structures theory. We construct the sl (2, R ) × R (ρ( t )) prolongation structure for an inhomogeneous equation of the reaction–diffusion type and give the corresponding AKNS-type equations and the Bäcklund transformation.
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Deng et al. (2007) studied this question.
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