H. Sanuki


SOKENDAI Lecture Series "Mathematics for Physics "Maghematical Tools for Nonlinear Phenomenta (Lecture series I)

Date of publication:

June 2006

Key words:

Typical nonlinear equations, analytical tools, non-secular perturbation method, multi-time expansion method, recductive perturbation method, Hopf-Cole transformation, Backlund transformation, Konno-Sanuki transformation, Steepest descent method, Van del pol equation, Mathieu equation, K-dV equation, Sine-Gordon equation, Nonlinear Schrodinger equation, 1D and "d-Solitons, Convective Cells


Mathematicla tools dealing with nonlinear phenomena are numerous and varied and have received much attention of many researchers during the last 100 years. Marvelous results obtained in plasma physics for past few years have actually enhanced its prestige and importnace of nonlinear physics considerably in the eyes of plasma fusion community. In this series of lectures, an attempt giving an introductory presentation of a variety of complementary methods and viewpoints that may be used in the study of broad spectrum of nonlinear phenomena is presented. The organization of this series of lectures consists of the three perspectives such as (1) mathematical tools of nonlinear phenomena, (2) WKB methods and related topics, and (3) mathematical topics associated with bifurcation phenomena. First, the mathematical tools of nonlinear phenomena (licture-1) are presented in theis article.

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