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We derive a nonlinear model for the pressure and flow velocity wave propagation in an arterial segment. We then study the transmission and reflection of pulses at bifurcation. We observe a linear dependence of the transmitted speeds to the incoming speeds, and similarly for the reflected speeds. We propose a method for validating the numerical results(More)
In this note we prove that the maximally defined operator associated with the Dirac-type differential expression M (Q) = i d dx Im −Q −Q * − d dx Im , where Q represents a symmetric m × m matrix (i.e., Q(x) ⊤ = Q(x) a.e.) with entries in L 1 loc (R), is J-self-adjoint, where J is the antilinear conjugation defined by J = σ 1 C, σ 1 = 0 Im Im 0 The(More)
The development of mathematical models for studying phenomena observed in vascular networks is very useful for its potential applications in medicine and physiology. Detailed 3D studies of flow in the arterial system based on the Navier-Stokes equations require high computational power, hence reduced models are often used, both for the constitutive laws and(More)
We study Darboux-type transformations associated with the fo-cusing nonlinear Schrödinger equation (NLS −) and their effect on spectral properties of the underlying Lax operator. The latter is a formally J-self-adjoint (but non-self-adjoint) Dirac-type differential expression of the form M (q) = i d dx −q −q − d dx , satisfying J M (q)J = M (q) * , where J(More)
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