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Functional analysis --- Differential equations, Nonlinear --- Nonlinear integral equations --- Numerical solutions. --- Functional analysis. --- Differential equations, Nonlinear - Numerical solutions. --- Nonlinear integral equations - Numerical solutions.

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The nonlinear Schrödinger equation is a prototypical dispersive nonlinear partial differential equation that has been derived in many areas of physics and analyzed mathematically for many years. With this book, we aim to capture different perspectives of researchers on the nonlinear Schrödinger equation arising from theoretical, numerical, and experimental aspects. The eight chapters cover a variety of topics related to nonlinear optics, quantum mechanics, and physics. This book provides scientists, researchers, and engineers as well as graduate and post-graduate students working on or interested in the nonlinear Schrödinger equation with an in-depth discussion of the latest advances in nonlinear optics and quantum physics.

Mathematical physics. --- Nonlinear integral equations. --- Integral equations, Nonlinear --- Integral equations --- Nonlinear theories --- Physical mathematics --- Physics --- Mathematics

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Differential equations --- 517.95 --- Differential equations, Nonlinear --- -Nonlinear integral equations --- -#KVIV --- Integral equations, Nonlinear --- Integral equations --- Nonlinear theories --- Nonlinear differential equations --- Partial differential equations --- Numerical solutions --- Nonlinear integral equations --- Numerical solutions. --- 517.95 Partial differential equations --- #KVIV --- Numerical analysis --- Differential equations, Nonlinear - Numerical solutions --- Nonlinear integral equations - Numerical solutions

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This book deals with solving mathematically the unsteady flame propagation equations. New original mathematical methods for solving complex non-linear equations and investigating their properties are presented. Pole solutions for flame front propagation are developed. Premixed flames and filtration combustion have remarkable properties: the complex nonlinear integro-differential equations for these problems have exact analytical solutions described by the motion of poles in a complex plane. Instead of complex equations, a finite set of ordinary differential equations is applied. These solutions help to investigate analytically and numerically properties of the flame front propagation equations.

Engineering. --- Appl.Mathematics/Computational Methods of Engineering. --- Plasma Physics. --- Engineering Fluid Dynamics. --- Engineering mathematics. --- Hydraulic engineering. --- Ingénierie --- Mathématiques de l'ingénieur --- Technologie hydraulique --- Combustion -- Mathematical models. --- Differential equations, Nonlinear. --- Nonlinear integral equations. --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Applied Mathematics --- Civil Engineering --- Combustion --- Mathematical models. --- Nonlinear differential equations --- Integral equations, Nonlinear --- Plasma (Ionized gases). --- Applied mathematics. --- Fluid mechanics. --- Integral equations --- Nonlinear theories --- Mathematical and Computational Engineering. --- Engineering, Hydraulic --- Engineering --- Fluid mechanics --- Hydraulics --- Shore protection --- Engineering analysis --- Mathematical analysis --- Mathematics --- Hydromechanics --- Continuum mechanics --- Gaseous discharge --- Gaseous plasma --- Magnetoplasma --- Ionized gases --- Plasma (Ionized gases)

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Many of problems of the natural sciences lead to nonlinear partial differential equations. However, only a few of them have succeeded in being solved explicitly. Therefore different methods of qualitative analysis such as the asymptotic methods play a very important role. This is the first book in the world literature giving a systematic development of a general asymptotic theory for nonlinear partial differential equations with dissipation. Many typical well-known equations are considered as examples, such as: nonlinear heat equation, KdVB equation, nonlinear damped wave equation, Landau-Ginzburg equation, Sobolev type equations, systems of equations of Boussinesq, Navier-Stokes and others.

Differential equations, Nonlinear --- Differential equations, Partial --- Equations aux dérivées partielles --- Asymptotic theory. --- Théorie asymptotique --- Electronic books. -- local. --- Equations. --- Nonlinear integral equations. --- Calculus --- Mathematics --- Physical Sciences & Mathematics --- Asymptotic theory --- Integral equations, Nonlinear --- Mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Integral equations. --- Partial differential equations. --- Physics. --- Analysis. --- Partial Differential Equations. --- Integral Equations. --- Theoretical, Mathematical and Computational Physics. --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Partial differential equations --- Equations, Integral --- Functional equations --- Functional analysis --- 517.1 Mathematical analysis --- Mathematical analysis --- Math --- Science --- Algebra --- Integral equations --- Nonlinear theories --- Global analysis (Mathematics). --- Differential equations, partial. --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Mathematical physics. --- Physical mathematics --- Physics --- Asymptotic theory in partial differential equations --- Asymptotic expansions --- Asymptotic theory in nonlinear differential equations