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A Course on Nonlinear Waves (Hardcover, 1993 ed.)
Loot Price: R3,073
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A Course on Nonlinear Waves (Hardcover, 1993 ed.)
Series: Nonlinear Topics in the Mathematical Sciences, 3
Expected to ship within 10 - 15 working days
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This volume presents a carefully written introduction to nonlinear
waves in the natural sciences and engineering. It contains many
classical results as well as more recent results, dealing with
topics such as the forced Korteweg--de Vries equation and material
relating to X-ray crystallography. The volume contains nine
chapters. Chapter 1 concerns asymptotics and nonlinear ordinary
differential equations. Conservation laws are discussed in Chapter
2, and Chapter 3 considers water waves. The scattering and inverse
scattering method is described in Chapter 4, which also contains a
full explanation of using the inverse scattering method for finding
1-, 2- and 3-soliton solutions of the Korteweg--de Vries equation.
After dealing with the Burgers equation in Chapter 5, Chapter 6
discusses the forced Korteweg--de Vries equations. Here the
emphasis is on steady-state bifurcations and unsteady-state
periodic soliton generation. The Sine--Gordon and nonlinear
SchrAdinger equations are the subject of Chapter 7. The final two
chapters consider wave instability and resonance. Every chapter
contains problems and exercises, together with guidance for their
solution. The volume concludes with some appendices which describe
symbolic derivations of certain results on solitons. Several
user-friendly MATHEMATICA packages are included. The prerequisite
for using this book is a background knowledge of basic physics,
linear algebra and differential equations. For graduates and
researchers in mathematics, physics and engineering wishing to have
a good introduction to nonlinear wave theory and its applications.
This volume is also highly recommended as a course book.
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