Titlebook: Nonlinear Partial Differential Equations for Scientists and Engineers; Lokenath Debnath Textbook 19971st edition Birkh?user Boston 1997 En

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ASTER

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 initia

類型

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.

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insolence

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

Abutment

Filibuster

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 dispersive term in the Korteweg-de Vries equation does prevent this from ever happening in its solution. In general, breaking can be prevented by including dispersive effects in

Comprise

,The Nonlinear Schr?dinger Equation and Solitary Waves,urbation approximation for the weakly and strongly nonlinear dispersive wave systems, respectively. This chapter is devoted to the nonlinear Schr?dinger equation and its solitary wave solutions. Several properties of the nonlinear Schr?dinger equation including envelope solitons and recurrence pheno