Titlebook: Nonlinear Partial Differential Equations for Scientists and Engineers; Lokenath Debnath Textbook 20052nd edition Birkh?user Boston 2005 En

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Linear Partial Differential Equations, problems in applied mathematics, mathematical physics, and engineering science. This subject plays a central role in modern mathematical sciences, especially in physics, geometry, and analysis. Many problems of physical interest are described by partial differential equations with appropriate initi

細(xì)胞膜

Nonlinear Model Equations and Variational Principles,wed by variational principles and the Euler-Lagrange equations. Also included are Plateau’s problem, Hamilton’s principle, Lagrange’s equations, Hamilton’s equations, the variational principle for nonlinear Klein-Gordon equations, and the variational principle for nonlinear water waves. Special atte

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First-Order Nonlinear Equations and Their Applications,nd 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

AMPLE

Conservation Laws and Shock Waves,n this chapter we study first-order, quasi-linear, partial differential equations which become conservation laws. We discuss the fundamental role of characteristics in the study of quasi-linear equations and then solve the nonlinear, initial-value problems with both continuous and discontinuous init

eustachian-tube

Endearing

,Nonlinear Dispersive Waves and Whitham’s Equations,ence of periodic wavetrains which are possible in nonlinear dispersive wave systems. He also determined that the dispersion relation on the amplitude produces significant qualitative changes in the behavior of nonlinear waves. It also introduces many new phenomena in the theory of dispersive waves,

CBC471

古文字學(xué)

Solitons and the Inverse Scattering Transform,r lead to breaking phenomena of the typical hyperbolic kind with the development of a vertical profile. In particular, the linear dispersive term in the Korteweg-de Vries equation prevents this from ever happening in its solution. In general, breaking can be prevented by including dispersive effects

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,The Nonlinear Schr?dinger Equation and Solitary Waves,anics, plasma physics, and nonlinear optics. The most common applications of the NLS equation include self-focusing of beams in nonlinear optics, modeling of propagation of electromagnetic pulses in nonlinear optical fibers which act as wave guides, and stability of Stokes waves in water. Some forma

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