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Algebro-geometric approach to nonlinear integrable equations
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In this paper, the authors introduce Riemann surfaces and theta functions as mathematical methods used to analyzse solitons, dynamical systems, phase transitions, etc, and to obtain the solutions of the related non-linear integrable equations.Abstract:
A brief but self-contained exposition of the basics of Riemann surfaces and theta functions prepares the reader for the main subject of this text, namely the application of these theories to solving non-linear integrable equations for various physical systems. Physicists and engineers involved in studying solitons, phase transitions or dynamical (gyroscopic) systems, and mathematicians with some background in algebraic geometry and Abelian and automorphic functions, are the targeted audience. This book is suitable for use as a supplementary text to a course in mathematical physics. The authors introduce Riemann surfaces and theta functions as mathematical methods used to analyzse solitons, dynamical systems, phase transitions, etc, and to obtain the solutions of the related non-linear integrable equations.read more
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Complex periodic potentials with real band spectra
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Riemann–Hilbert problems and N-soliton solutions for a coupled mKdV system
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