\documentclass{letterca2}

\name{Cornelis van der Mee}
\location{viale Merello 92, 09123 Cagliari, Italia}
\fax{+39-070-6755601}
\town{Cagliari, }
\telephone{011-39-070-6755605}
\fax{011-39-070-6755601}
\email{cornelis@krein.unica.it}
%\signature{}

%\makelabels

\begin{document}

\begin{letter}{
Dr. Sarbarish Chakravarty\\
Chair, Primary Unit Evaluation Committee\\
Department of Mathematics\\
University of Colorado\\
1420 Austin Bluffs Parkway\\
Colorado Springs, CO 80918\\
%email chuck@math.uccs.edu, (719) 255-3549
}

\opening{}

\vspace{12pt}

I am writing this letter on Dr. Barbara Prinari's request for tenure. I shall
first discuss her research qualifications and then go on to assess her other
contributions to your department and the scientific community.

Dr. Barbara Prinari has an outstanding research record on nonlinear wave
equations, soliton solutions, and integrable systems. Her research on these
topics primarily regards four important areas: 1)~Kadomtsev-Petviashvili
equation, 2)~(matrix) nonlinear Schr\"o\-din\-ger equations with vanishing
boundary conditions, 3)~(matrix) nonlinear Schr\"o\-din\-ger equations with
nonvanishing boundary conditions, and 4)~discrete integrable systems.

The inverse scattering transform of the Kadomtsev-Petviashvili equation, a $2+1$
integrable equation existing in the two flavors KPI and KPII, and the
derivation of various special solutions (line solitons, $N$-soliton solutions)
form the main arguments of her Ph.D. thesis in physics at the University of
Lecce, Italy, written under the supervision of Professors Marco Boiti and Flora
Pempinelli. Her main contribution has been the introduction of the extended
resolvent method to formulate the inverse scattering transform, especially
since traditional approaches based on the analyticity of Jost solutions and the
solution of integral equations proved difficult to generalize to $2+1$ nonlinear
evolution equations.

Dr. Prinari's research on (matrix) nonlinear Schr\"o\-din\-ger equations with
vanishing boundary conditions has led to important results on vector soliton
interactions. In collaboration with Professors Mark Ablowitz and Javier
Villarroel, she has also obtained interesting results on the unique solvability
of the corresponding direct and inverse scattering problems and partial results
on the characterization of those scattering data which lead to integrable
Zakharov-Shabat potentials.

In my opinion, Dr. Prinari's most impressive research and definitely the
research that has had the major impact on the direction the research at my home
university of Cagliari, regards (matrix) nonlinear Schr\"o\-din\-ger
equations with nonvanishing boundary conditions and discrete integrable
systems. Here the term ``impressive" does not only pertain to the results
obtained and to the difficulty of the two problems, but foremost to the
interesting questions she has, directly or indirectly, raised.

The inverse scattering transform of the (matrix) nonlinear Schr\"o\-din\-ger
equation with nonvanishing boundary conditions is a very difficult problem,
because the continuous spectrum of the accompanying linear eigenvalue equation,
the (matrix) Zakharov-Shabat system, has nonuniform spectral multiplicity. In
the defocusing case, relevant to the propagation of signals in fiber optics
under normal dispersion conditions, this has led to very different approaches
to the $1+1$, $1+2$, and $1+N$ (with $N\ge2$) cases. In collaboration with
Professors Mark Ablowitz and Gino Biondini, she has made significant
contributions in all of these three cases. Established inverse scattering
transform methods had to be redeveloped from first principles, especially in the
$1+N$ case.

In the beginning of her scientific career, Dr. Barbara Prinari has produced
several papers on the inverse scattering transform of discretizations of the
sine-Gordon and Korteweg-de Vries equations. However, her major contribution in
this field regards her work on the matrix generalization of the
Ablowitz-Ladik discretization of the nonlinear Schr\"o\-din\-ger equation. This
particular discretization has created its own mathematical problems. Together
with Professors Mark Ablowitz and David Trubatch, she has been producing
an impressive amount of research material on which subsequent researchers, as
well as she herself, can build.

Dr. Barbara `Prinari's major contribution to the field of integrable systems has
been the 2004 monograph written in collaboration with Professors Mark Ablowitz
and David Trubatch. In its five chapters, a complete outline is given of the
inverse scattering transforms of the (matrix) nonlinear Schr\"o\-din\-ger (NLS)
equation and the (matrix) integrable discrete nonlinear Schr\"o\-din\-ger
(IDNLS) equations, devoting separate chapters to the scalar and the matrix
versions of the same equation. This monograph has touched the scientific life
of various researchers in the field, myself included, and suggested interesting
problems for further investigation.

Dr. Barbara Prinari has produced almost 30 papers in highly rated international
journals such as Acta Applicandae Mathematicae, Inverse Problems, Journal of
Mathematical Physics, Journal of Physics A, Mathematical and Computer Modelling,
Physics Letters A, Proceedings of the Steklov Institute of Mathematics, 
Studies in Applied Mathematics, and Theoretical and Mathematical Physics. She
has no papers in journals with soft or nonexistent refereeing. She has produced
good quality papers with 14 different co-authors, including a top researcher
like Mark Ablowitz. Her flow of papers does not seem to slow down.
\bigskip

Let us now discuss Dr. Prinari's service to UCCS and to the scientific
community.
\begin{itemize}
\item[$\bullet$] Her research funding from non-UTA sources consists of an NSF
grant and participation in several competitive Italian Ministery of Education
(MIUR) grants. Moreover, a two year research grant proposal submitted by her in
collaboration with people from my own university, has been funded by the
Autonomous Region of Sardinia. She has also been a panel member to review NSF
grant proposals.
\item[$\bullet$] Her role in organizing conferences has consisted of organizing
eight special sessions. She has been a regular participant in international
workshops and conferences.
\item[$\bullet$] She has taught a variety of courses in Italy and the United
States on subjects as diverse as calculus, complex analysis, differential
equations, linear algebra, and introductory physics. At conferences and invited
lectures she has attracted the attention for the clearness of her presentation.
\end{itemize}

I have written several letters to support a request for tenure or a request for
promotion for full professor. Writing a letter on behalf of Dr. Barbara Prinari
has been by far the easiest letter I had to write, because there are simply no
apparent weaknesses in her resume.  She has been a great inspiration for other
researchers (myself included), postdocs, and students. She would be a great
asset to your department.
\vspace{36pt}

\par\noindent Cornelis van der Mee \hfill Sincerely yours,
\par\noindent Full Professor of Mathematical Physics
\par\noindent Dept. of Mathematics and Computer Science
\par\noindent University of Cagliari
\par\noindent Viale Merello 92, 09123 Cagliari, Italy

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\end{letter}

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