Professor

Nonlinear waves; integrable systems; solitons; mathematical modeling in social and behavioral science.

PhD in Physics (1999), University of Lecce, Italy

The study of wave phenomena by means of mathematical models often leads to a certain class of nonlinear partial differential equations referred to as integrable systems.

My main area of research deals with nonlinear waves and integrable systems, and has concerned both the study of the integrability of certain nonlinear partial differential equations and their discretizations (differential-difference equations), and of the properties of these equations and their solutions. Specific problems that I have addressed are: the development of the Inverse Scattering Transform (IST) as a tool to solve the initial-value problem for scalar, vector and matrix continuous and discrete nonlinear Schrodinger (NLS) equations with both vanishing and nonvanishing boundary conditions at infinity; solitons and rogue wave solutions; vector soliton interactions, etc. Other integrable systems I have studied over the years include: short-pulse systems, Maxwell-Bloch equations, the Kadomtsev-Petviashvili equations in 2 spatial dimensions, etc.

I have also been interested in mathematical models for social and behavioral sciences. We have applied generalized kinetic methods and artificial neural networks to analyze and control the quality of an existing neuropsychiatric ward. Recently, we also developed a dynamical systems model for triadic reciprocal determinism, to study how a person experiences stress or traumatic events, and the interplay among coping self-efficacy, behavior and the perception of external environment.

**Book**

- M.J. Ablowitz, B. Prinari, A.D. Trubatch, Discrete and Continuous Nonlinear Schrödinger Systems, LMS Lecture Notes Series 302, Cambridge University Press (2004)

Refereed Articles

- B. Prinari, “Inverse Scattering Transform for nonlinear Schrödinger system on a nontrivial background: a survey of classical results, new developments and future directions”, J. Nonlin. Math. Phys. 30, 317-383 (2023) [invited review article]
- B. Prinari, A.D. Trubatch, and B-Feng Feng, “Inverse scattering transform for the complex short-pulse equation by a Riemann-Hilbert approach”, Eur. Phys. J. Plus, 135, 716 (2020)
- M. Lo Schiavo, B. Prinari, I. Saito, K. Shoji, and C.C. Benight, “A deterministic dynamical system approach to triadic reciprocal determinism of social cognitive theory”, Math. Comp. Simul., 159, 18-38 (2019)
- B. Prinari, F. Demontis, S. Li and T.P. Horikis, “Inverse scattering transform and soliton solutions for a square matrix nonlinear Schrödinger equation with nonzero boundary conditions, Physica D 368, pp 22-49 (2018)
- G. Biondini, D.K. Kraus, B. Prinari, “The three-component defocusing nonlinear Schrödinger equation with nonzero boundary conditions”, Comm. Math. Phys. 348, pp. 475-533 (2016)
- B. Prinari, “Discrete solitons of the Ablowitz-Ladik equation with nonzero boundary conditions via inverse scattering”, J. Math. Phys. 57, 083510 (2016)
- B. Prinari, F. Vitale and G. Biondini, “Dark-bright soliton solutions with nontrivial polarization interactions for the three-component defocusing nonlinear Schrödinger equation with nonzero boundary conditions”, J. Math. Phys. 56, 071505 (2015) [selected as featured article for the July 2015 issue of JMP]
- M. Lo Schiavo, B. Prinari, J.A. Gronski and A.V. Serio, “An artificial neural network approach for modelling the ward atmosphere in a medical structure”,
*Math. Comp. Simul.*116, pp. 44-58 (2015) - F. Demontis, B. Prinari, C. van der Mee, F. Vitale, “The inverse scattering transform for the defocusing nonlinear Schrödinger equation with nonzero boundary conditions”, Stud. App. Math. 131, pp. 1-40 (2013)
- B. Prinari, G. Biondini and A.D. Trubatch, “Inverse scattering transform for the multicomponent nonlinear Schrödinger equation with nonzero boundary conditions at infinity”, Stud. App. Math. 126 (3), pp. 245-302 (2011)
- M. Lo Schiavo, B. Prinari and A.V. Serio, “Mathematical modeling of quality in a medical structure: A case study”,
*Math. Comp. Mod.*54, pp. 2087-2103 (2011) - B. Prinari, M.J. Ablowitz and G. Biondini, “Inverse scattering transform for the vector nonlinear Schrödinger equation with non-vanishing boundary conditions”, J. Math. Phys. 47, 063508, 33pp (2006)