Luigi Martina

Biography

Born in 1957, a former researcher since 1985, Associate Professor of Theoretical Physics at the MFN Sciences at the University of Lecce since 2001. He published 90 articles in press, international scientific journals with referee, and conference papers. He has published some dissertation work on and about the teaching of Physics. He has written 4 volumes of international conference papers and has written a monograph, with G. Soliani, on Quantum Computation. Its main scientific interests concern: 1) integrability conditions, equivalence gauge and nonlinear PED's Hamiltonian structures; 2) dynamics of electron beams photographed; 3) Backlund Transformation Applications, which led to the discovery of 2 + 1 size solitons; 4) timing symmetry groups and their generalizations for ODE's, PDEs, and equations to nonlinear differences; 5) models of spin planar integrable, vortices, contradictions and theories of Chern-Simons, even in non-commutative plans; 6) Exotic galilean symmetry in 2 + 1 dimensions; 7) semiclassical approximation and geometric phase; 8) Continuous and discrete integrable surfaces and their applications to biophysics and biomedical diagnostics; 9) quantum computation. He has collaborated with several foreign researchers, carrying out research activities at the University of Montreal (Canada), the Univ. du Languedoc (France) and the Univ. de Tours (France), where he was Prof. Invité. He has participated in numerous national and international research projects and has been the coordinator of NATO CRG 960717. He is referee for several scientific journals in physics-mathematics. After having held courses in Physics Gen and Institutions of F. Theor, Quantum Mechanics and Applications, Symbolic Calculation, Mathematical Methods. of the Sist. Nonlinear. Didactics of Physics I for the SSIS-Puglia School. He currently holds courses in Theoretical Physics (L. Physics Spec.) And Advanced Quantum Mechanics for the PhD in Physics. He is actively involved in the dissemination of Physics.

Research Interest

I) A vast array of mathematical models, extracted from various phenomenological contexts, express themselves in terms of classical nonlinear evolutionary PDEs. It is remarkable that some of their classes of solutions, such as vortexes and solitons, are stable and localized in space and, because of their reciprocal interaction properties, can be considered as quasi-particle excitations of the theory. The stability of the solutions can be ensured by a sufficient number of laws of conservation, or by the existence of topological indices, which prevent it from decaying in a linear overlap of elementary excitations. In the exceptional, but important, cases "fully integrable" there is a complete set of inversion integrals, and multi-solitonic solutions can be calculated using analytical techniques: Bäcklund transformations and inverse spectral transformation. These systems possess a very rich symmetry structure (Lie-Bäcklund), as well as being bi-hamiltonians, so that this property is assumed as a tool to verify the degree of integrity of a given equation. Although there are important examples in 2- or 3 + 1 dimensions, such as KP, mKP, Davey-Stewartson, Kaup-Kuperschmidt, 2D Sawada-Kotera, Nizhnik-Veselov-Novikov, 2DLong-Wave and other hydrodynamic systems , the theory of the symmetry property of these systems is much less developed due to the generally non-local character of generalized symmetries and conservation laws. However, Group analysis methods remain a very powerful set of tools, especially if their generalizations are considered to be beyond the simple Lie symmetry symmetries on the basis of the theory of diffractive invariants, such as the group spacing of the solution space, the search for partially invariant solutions, conditioned symmetries, non-classical symmetries, potential symmetries, lambda and symmetry, non-local symmetries, variational symmetries, twisted symmetries, symmetries in non-commutative spaces (see II)). These methods, associated with other analytical and topological ones, may be fruitful to investigate multi-component systems and 2 or 3 spatial dimensions, which have localized solutions that are particularly relevant to them.