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Barbara Prinari receives UB Exceptional Scholar Award for Sustained Achievement

The Department of Mathematics congratulates Professor Barbara Prinari on receiving the 2026 UB Exceptional Scholar Award for Sustained Achievement. Prinari’s main area of research deals with nonlinear waves and integrable systems, and has focused on both the study of the integrability of certain nonlinear partial differential equations and their discretizations (differential-difference equations), as well as the properties of these equations and their solutions. Prinari’s research also explores how mathematical models can be used for social and behavioral sciences. She recently 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.

The UB Exceptional Scholar Award for Sustained Achievement was established in 2002 to honor outstanding professional achievement focused on a particular body of work over a number of years. The award recognizes an unprecedented accomplishment in a senior scholar's career, distinguishing a body of work of enduring importance that has gone beyond the norm in a particular field of study.

In 2025, Prinari won the prestigious Fulbright Scholar Award. The award supports Prinari's travel to Greece to study wave phenomena. The main goal of the collaborative research that Prinari will conduct at the University of Ioannina will be to develop a rigorous direct perturbation theory for the study of dark-bright solitons under physically relevant perturbations (e.g., dissipation, linear and nonlinear loss).

Faculty Profile

Barbara Prinari

PhD

Barbara Prinari.

Barbara Prinari

PhD

Barbara Prinari

PhD

Research Interests

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

Education

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

Research Summary

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.

Selected Publications

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)