Asymptotic Methods and Nonlinear Evolution Equations

Lokenath Debnath ()
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Lokenath Debnath: University of Texas, Pan American, Department of Mathematics

Chapter 12 in Nonlinear Partial Differential Equations for Scientists and Engineers, 2012, pp 623-674 from Springer

Abstract: Abstract Many physical systems involving nonlinear wave propagation include the effects of dispersion, dissipation, and/or the inhomogeneous property of the medium. The governing equations are usually derived from conservation laws. In simple cases, these equations are hyperbolic. However, in general, the physical processes involved are so complex that the governing equations are very complicated, and hence, are not integrable by analytic methods. So, special attention is given to seeking mathematical methods which lead to a less complicated problem, yet retain all of the important physical features. In recent years, several asymptotic methods have been developed for the derivation of the evolution equations which describe how some dynamical variables evolve in time and space.

Keywords: Dispersion Relation; Multiple Scale; Burger Equation; Nonlinear Evolution Equation; Boussinesq Equation (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/978-0-8176-8265-1_12

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