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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations
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Nonlinear Waves: A Geometrical Approach (Hardcover)
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Nonlinear Waves: A Geometrical Approach (Hardcover)
Series: Series On Analysis, Applications And Computation, 9
Expected to ship within 10 - 15 working days
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This volume provides an in-depth treatment of several equations and
systems of mathematical physics, describing the propagation and
interaction of nonlinear waves as different modifications of these:
the KdV equation, Fornberg-Whitham equation, Vakhnenko equation,
Camassa-Holm equation, several versions of the NLS equation,
Kaup-Kupershmidt equation, Boussinesq paradigm, and Manakov system,
amongst others, as well as symmetrizable quasilinear hyperbolic
systems arising in fluid dynamics.Readers not familiar with the
complicated methods used in the theory of the equations of
mathematical physics (functional analysis, harmonic analysis,
spectral theory, topological methods, a priori estimates,
conservation laws) can easily be acquainted here with different
solutions of some nonlinear PDEs written in a sharp form (waves),
with their geometrical visualization and their interpretation. In
many cases, explicit solutions (waves) having specific physical
interpretation (solitons, kinks, peakons, ovals, loops, rogue
waves) are found and their interactions are studied and
geometrically visualized. To do this, classical methods coming from
the theory of ordinary differential equations, the dressing method,
Hirota's direct method and the method of the simplest equation are
introduced and applied. At the end, the paradifferential approach
is used.This volume is self-contained and equipped with simple
proofs. It contains many exercises and examples arising from the
applications in mechanics, physics, optics and, quantum mechanics.
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