Titlebook: Nonlinear Partial Differential Equations for Scientists and Engineers; Lokenath Debnath Textbook 2012Latest edition Springer Science+Busin

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First-Order, Quasi-linear Equations and Method of Characteristics,ions. From a mathematical point of view, first-order equations have the advantage of providing a conceptual basis that can be utilized for second-, third-, and higher-order equations..This chapter is concerned with first-order, quasi-linear and linear partial differential equations and their solutio

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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

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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 ini

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,Nonlinear Diffusion–Reaction Phenomena,sical point of view, the convection–diffusion process and the diffusion–reaction process are quite fundamental in describing a wide variety of problems in physical, chemical, biological, and engineering sciences. Some nonlinear partial differential equations that model these processes provide many n

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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 Schrödinger Equation and Solitary Waves,ics, 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 formal

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,Nonlinear Klein–Gordon and Sine-Gordon Equations,s methods of solutions of these equations. The Green function method combined with integral transforms is employed to solve the linear Klein–Gordon equation. The Whitham averaging procedure and the Whitham averaged Lagrangian principle are used to discuss solutions of the nonlinear Klein–Gordon equa