SARA LOMBARDO

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Sara Lombardo

EPSRC Research Fellow

Senior Lecturer in Applied Mathematics
Email: sara dot lombardo at northumbria dot ac dot uk

Research

My main research interests are in Applied Mathematics, in particular in the theory of Integrable Systems.

My research activity concerns symmetries, coherent structures (solitons), algebraic structures of integrable equations (Lie (super) algebras); nonlinear integrable equations and their applications to physics (mainly nonlinear optics) and to selected biophysical systems.

Most of my research accomplishments regard the analysis of nonlinear PDEs (both from a theoretical view point and for applications). My contribution in this area has been to classify special algebraic and rational solutions of integrable equations, to produce new examples of this class of nonlinear differential equations and to study the asymptotic behaviour of their solutions.
My current research is also centred around the theory of Automorphic Lie Algebras and related integrable equations. This is a recently discovered class of infinite dimensional Lie algebras, called Automorphic Lie Algebras because of their analogy with the classical theory of automorphic functions. Their discovery was motivated by the theory of integrable equations but their applications go far beyond it (from geometry and quantum field theory) and make them interesting as algebraic objects in their own right.

Nonlinear wave equations and Integrability

Multicomponent integrable waves equations

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Nonlinear waves in shallow waterDarboux Dressing Transformations for multicomponent wave equations have been developed to compute solitonic solutions of systems of coupled PDEs. Various applications to Nolinear Optics have been studied.

Collaborations: Antonio Degasperis (Università degli Studi di Roma "La Sapienza", Roma, Italy), Fabio Baronio, Matteo Conforti, Stefano Wabnitz (CNISM, Universitá degli Studi di Brescia, Italy)

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Coherent structures

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Automorphic Lie Algebras

IcosahedronAutomorphic Lie Algebras associated to finite groups

Classification

This is an exciting research programme, at the crossroad between Pure and Applied Mathematics, aimed to a full classification and description of a new class of infinite dimensional Lie Algebras.

Collaborations: Jan A Sanders (Vrije Universiteit Amsterdam, The Netherlands), Alexander Mikhailov (University of Leeds, UK)

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Events

NEEDS 2012

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Nonlinear Evolution Equations and Dynamical Systems
NEEDS 2012 will be held at the Orthodox Academy of Crete, in Kolymvari, Chania (Crete, Greece), from 8 to 15 July 2012.
See NEEDS 2012 web page for more information.

Science Festival

Newcastle Science Festival

LMS Northem Meeting

LMS Northern Regional Meeting
6-8 June 2012

Mathematical Modelling Lab

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Studentships

To appear soon

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