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Nonlinear Waves: An Introduction (Hardcover)
Loot Price: R1,891
Discovery Miles 18 910
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Nonlinear Waves: An Introduction (Hardcover)
Series: Series On Analysis, Applications And Computation, 4
Expected to ship within 12 - 17 working days
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Total price: R1,911
Discovery Miles: 19 110
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This book deals with equations of mathematical physics as the
different modifications of the KdV equation, the Camassa-Holm type
equations, several modifications of Burger's equation, the
Hunter-Saxton equation and others. The equations originate from
physics but are proposed here for their investigation via purely
mathematical methods in the frames of university courses. More
precisely, the authors propose classification theorems for the
traveling wave solutions for a sufficiently large class of third
order nonlinear PDE when the corresponding profiles develop
different kind of singularities (cusps, peaks). The orbital
stability of the periodic solutions of traveling type for mKdV
equations are also studied. Of great interest too is the
interaction of peakon type solutions of the Camassa-Holm equation
and the solvability of the classical and generalized Cauchy problem
for the Hunter-Saxton equation. The Riemann problem for special
systems of conservation laws and the corresponding d-shocks are
also considered. At the end of the book the authors study the
interaction of two piecewise smooth waves in the case of two space
variables and they verify the appearance of logarithmic
singularities. As it concerns numerical methods in the case of
periodic waves the authors apply Cellular Neural Network (CNN)
approach.
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