Mark J. Ablowitz

Jay Mark Ablowitz ( born June 5, 1945 in New York City ) is an American applied mathematician who deals with solitons.

Life

Ablowitz studied at the University of Rochester ( BA, 1967) and in 1971 at the Massachusetts Institute of Technology David Benney PhD ( Non-Linear Dispersive Waves and multi-phase modes). From 1967 to 1971 he was a teaching assistant at MIT. From 1971, he was first an assistant professor, associate professor in 1975 and 1976 professor at Clarkson University. 1979-1985 he was there Board of mathematics faculty and dean from 1985 to 1989. From 1989 he was professor at the University of Colorado at Boulder and up to 2000 there Head of Applied Mathematics.

1977/78 and 1984 he was Visiting Professor of Applied Mathematics at Princeton University and 1984 exchange scientists of the National Academy of Sciences in the Soviet Union. In 1979 he was Co- Director of the Joint Symposium on soliton theory, the U.S. and Soviet Academies of Sciences. In 1985 he was a visiting scientist at the Institute of Theoretical Physics of the University of California, Santa Barbara.

From 1975 to 1977 he was a Sloan Fellow and Guggenheim Fellow in 1984. In 1976 he was awarded the Graham Clarkson Research Award. From 1976 to 1979 he was associate editor of the Journal of Mathematical Physics.

He has been married since 1968 and has three children.

Work

It deals with the inverse scattering transform ( Inverse Scattering Transform, IS ), a fundamental solution method of certain nonlinear partial differential equation ( in one or two spatial dimensions, for example, scalar and vector nonlinear Schrödinger equations), the conceptually similar to the Fourier transform in the linear case is. A named after him, Ramani and Segur Harvey conjecture states that non-linear partial differential equations are solved only by the IS, if their derived by reducing ordinary differential equations have the Painlevé property. With others, he showed that the self-dual Yang-Mills equations, which play a central role in the theory of integrable systems after reduction not only provide most of the known Soliton Equations, but also non-linear differential equations that Jean Chazy 1909 examined and also compounds studies of S. Ramanujan 1916.

Ablowitz researching a lot about applications of solitons in optics and quantum optics ( dynamics of ultrashort pulses in mode-locked lasers, communication in optical fibers with very high bitrate, nonlinear optical waveguides ). He also conducted research on dispersive shock wave (DSW, dispersive shock waves ) and water waves.

Writings

  • Harvey Segur Solitons and the Inverse Scattering Transform, SIAM Studies in Applied Mathematics, 1981
  • Editor with B. Fuchs Steiner, Martin Kruskal Topics in Soliton Theory and Exactly Solvable Nonlinear Equations, World Scientific 1987
  • PA Clarkson Solitons, Nonlinear Evolution Equations and Inverse Scattering, London Mathematical Society Lecture Notes Series, Volume 149, Cambridge University Press 1991
  • Athanassios S. Fokas Complex Variables with: Introduction and Applications, Cambridge University Press, 1997
  • With M. Boiti, F. Pempinelli, B. Prinari: Nonlinear Physics: Theory and Experiment. II, World Scientific 2003
  • With B. Prinari, AD Discrete and Continuous Nonlinear Schrödinger Trubatch Systems, Cambridge University Press, 2004
  • Nonlinear dispersive waves: Asymptotic Analysis and Solitons, Cambridge University Press 2011
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