First-Order Nonlinear Equations and Their Applications

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

Chapter 4 in Nonlinear Partial Differential Equations for Scientists and Engineers, 2012, pp 227-256 from Springer

Abstract: Abstract First-order, nonlinear, partial differential equations arise in various areas of physical sciences which include geometrical optics, fluid dynamics, and analytical dynamics. An important example of such equations is the Hamilton–Jacobi equation used to describe dynamical systems. Another famous example of the first-order nonlinear equations is the eikonal equation which arises in nonlinear optics and also describes the propagation of wave fronts and discontinuities for acoustic wave equations, Maxwell’s equations, and equations of elastic wave propagation. Evidently, first-order, nonlinear equations play an important role in the development of these diverse areas.

Keywords: First-order Nonlinear Equations; Hamilton-Jacobi Equation; Lagrange Brackets; Monge Cone; Solution Surface (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/978-0-8176-8265-1_4

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