Nonlinear Waves (MAGIC021)
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This course is part of the MAGIC core.
The aim of this module is to introduce students to the major ideas and techniques in the nonlinear wave theory (see the Syllabus).
Spring 2019 (Monday, January 21 to Friday, March 29)
No specific requirements. Standard undergraduate courses in analysis, mathematical methods and partial differential equations are desirable.
The aim of this module is to introduce major ideas and techniques of modern nonlinear wave theory, with an emphasis on asymptotic methods for nonlinear dispersive PDEs and applied aspects of integrability and inverse scattering transform.
MAGIC 021: Nonlinear Waves (20 hours)
Lecturers: R.H.J. Grimshaw, G.A. El, K.R. Khusnutdinova
 Whitham, G.B. 1974 Linear and Nonlinear Waves, Wiley, New York.
 Ablowitz, M.J. & Segur, H. 1981 Solitons and the Inverse Scattering Transform, SIAM.
 Dodd, R.K., Eilbeck, J.C., Gibbon, J.D. & Morris, H.C. 1982 Solitons and Nonlinear Waves Equations, Academic Press, Inc.
 Novikov, S.P., Manakov, S.V., Pitaevskii, L.P. & Zakharov, V.E. 1984 The Theory of Solitons: The Inverse Scattering Method, Consultants, New York.
 Newell, A.C. 1985 Solitons in Mathematics and Physics, SIAM.
 Drazin, P.G. & Johnson R.S. 1989 Solitons: an Introduction, Cambridge University Press,
 Scott, A. 1999 Nonlinear Science: Emergence and Dynamics of Coherent Structures, Oxford University Press Inc., New York.
 Kamchatnov, A.M. 2000 Nonlinear Periodic Waves and Their Modulations-An Introductory Course, World Scientific, Singapore.
 Kivshar, Y.S., Agrawal, G. 2003 Optical Solitons: From Fibers to Photonic Crystals, Elsevier Science, USA.
 Braun, O.M., Kivshar, Y.S. 2004 The Frenkel-Kontorova model. Concepts, methods, and applications. Springer, Berlin.
 Grimshaw, R. (ed.). 2005 Nonlinear Waves in Fluids: Recent Advances and Modern Applications. CISM Courses and Lectures, No. 483, Springer, Wien, New York.
 Grimshaw, R. (ed.) 2007 Solitary Waves in Fluids. Advances in Fluid Mechanics, Vol 47, WIT Press, UK.
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Assessment for this course will be via a single take-home paper with 2 weeks to complete and submit online. To pass the exam one is required to complete at least 3 out of 4 questions and to obtain at least 50
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