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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations
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Nonlinear Dispersive Equations - Inverse Scattering and PDE Methods (Hardcover, 1st ed. 2021)
Loot Price: R2,289
Discovery Miles 22 890
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Nonlinear Dispersive Equations - Inverse Scattering and PDE Methods (Hardcover, 1st ed. 2021)
Series: Applied Mathematical Sciences, 209
Expected to ship within 12 - 19 working days
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Nonlinear Dispersive Equations are partial differential equations
that naturally arise in physical settings where dispersion
dominates dissipation, notably hydrodynamics, nonlinear optics,
plasma physics and Bose-Einstein condensates. The topic has
traditionally been approached in different ways, from the
perspective of modeling of physical phenomena, to that of the
theory of partial differential equations, or as part of the theory
of integrable systems. This monograph offers a thorough
introduction to the topic, uniting the modeling, PDE and integrable
systems approaches for the first time in book form. The
presentation focuses on three "universal" families of physically
relevant equations endowed with a completely integrable member: the
Benjamin-Ono, Davey-Stewartson, and Kadomtsev-Petviashvili
equations. These asymptotic models are rigorously derived and
qualitative properties such as soliton resolution are studied in
detail in both integrable and non-integrable models. Numerical
simulations are presented throughout to illustrate interesting
phenomena.By presenting and comparing results from different
fields, the book aims to stimulate scientific interactions and
attract new students and researchers to the topic. To facilitate
this, the chapters can be read largely independently of each other
and the prerequisites have been limited to introductory courses in
PDE theory.
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