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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)

We investigate the well-posedness of a class of nonlinear dispersive waves on trees, in connection with the mathematical modeling of the human cardiovascular system. Specifically, we study the Benjamin-Bona-Mahony (BBM) equation , also known as the regularized long wave equation, posed on finite trees, together with standard junction and terminal boundary… (More)

- RADU CASCAVAL
- 2008

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)

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)

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