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We apply the mathematical technique of factorization of differentialoperators to two different problems. First we review our results related to thesupersymmetry of the Montroll kinks moving onto the microtubule walls as wellas mentioning the sine-Gordon model for the microtubule nonlinear excitations.Second, we find analytic expressions for a class of one-parameter solutions ofa sort of diffusion equation of Bessel type that is obtained by supersymmetryfrom the homogeneous form of a simple damped wave equations derived in theworks of P.A. Robinson and collaborators for the corticothalamic system. Wealso present a possible interpretation of the diffusion equation in the braincontext

Supersymmetric methods in the traveling variable: inside neurons and at the brain scale