Barbara Prinari, co-founder and deputy editor, Cambridge Journal of Nonlinear Waves
Journal of Nonlinear Waves, poster courtesy of Cambridge Core, 2024. ISSN: 3033-4268 (Online) Frequency: 1 issue per year.
Published September 9, 2024
The UB Department of Mathematics is pleased to announce that Professor Barbara Prinari is co-founder and deputy editor of Cambridge Core's Journal of Nonlinear Waves. Prinari's research adds scope and depth to the journal's editorial board. Problems addressed by Prinari include 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.
Journal of Nonlinear Waves
Journal of Nonlinear Waves is the home for the field of nonlinear wave phenomena, broadly defined. It publishes authoritative articles on theoretical and computational aspects of nonlinear waves grounded in applications, as well as on experimental investigations that have direct connection to the mathematics of nonlinear waves. The journal invites papers on fundamental contributions to nonlinear waves and applications in many physical settings including optics, condensed matter, fluid dynamics, geophysics, material science, plasma physics, and biological systems.
Article topics include:
- Nonlinear waves in the physical and applied sciences (optics, condensed matter, fluid dynamics, solid state and materials science, and geophysics/atmospheric/plasma physics, and biology)
- Applied integrable and non-integrable systems
- Dispersive hydrodynamics
- Solitary waves and soliton theory
- Deterministic and random nonlinear wave phenomena (e.g., wave or soliton turbulence)
- Nonlinear waves in lattices
- Numerical methods (including ML/AI-based ones) for nonlinear waves models.
- Scientific computation and data-driven methods for nonlinear waves.
- Asymptotic and variational methods for nonlinear waves problems
- Modelling and experiments related to nonlinear waves
- Dynamical systems approaches to nonlinear waves problems
- Nonlinear wave modulation theory
- Nonlinear waves in dissipative systems
- Stability of nonlinear waves
- Lagrangian and Hamiltonian nonlinear wave mechanics
Learn more about the journals editorial board, here.
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Faculty Profile
Barbara Prinari
PhD
Professor
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)