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nonlinear differential equation

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  • Nonlinear Schrödinger equation — This page is about the equation iψt = −½ψxx + κ|ψ|2ψ. For the equation iψt = −½ψxx + V(x)ψ + κ|ψ|2ψ, used in Bose–Einstein condensate theory, see Gross–Pitaevskii equation. In theoretical physics, the nonlinear Schrödinger equation (NLS) is a… …   Wikipedia

  • Differential equation — Not to be confused with Difference equation. Visualization of heat transfer in a pump casing, created by solving the heat equation. Heat is being generated internally in the casing and being cooled at the boundary, providing a steady state… …   Wikipedia

  • Partial differential equation — A visualisation of a solution to the heat equation on a two dimensional plane In mathematics, partial differential equations (PDE) are a type of differential equation, i.e., a relation involving an unknown function (or functions) of several… …   Wikipedia

  • Stochastic differential equation — A stochastic differential equation (SDE) is a differential equation in which one or more of the terms is a stochastic process, thus resulting in a solution which is itself a stochastic process. SDE are used to model diverse phenomena such as… …   Wikipedia

  • Ordinary differential equation — In mathematics, an ordinary differential equation (or ODE) is a relation that contains functions of only one independent variable, and one or more of their derivatives with respect to that variable. A simple example is Newton s second law of… …   Wikipedia

  • Delay differential equation — In mathematics, delay differential equations (DDEs) are a type of differential equation in which the derivative of the unknown function at a certain time is given in terms of the values of the function at previous times. A general form of the… …   Wikipedia

  • Hyperbolic partial differential equation — In mathematics, a hyperbolic partial differential equation is usually a second order partial differential equation (PDE) of the form :A u {xx} + 2 B u {xy} + C u {yy} + D u x + E u y + F = 0 with: det egin{pmatrix} A B B C end{pmatrix} = A C B^2 …   Wikipedia

  • Dispersive partial differential equation — In mathematics, a dispersive partial differential equation or dispersive PDE is a partial differential equation that is dispersive. In this context, dispersion means that waves of different wavelength propagate at different phase velocities.… …   Wikipedia

  • Parabolic partial differential equation — A parabolic partial differential equation is a type of second order partial differential equation, describing a wide family of problems in science including heat diffusion and stock option pricing. These problems, also known as evolution problems …   Wikipedia

  • List of partial differential equation topics — This is a list of partial differential equation topics, by Wikipedia page. Contents 1 General topics 2 Specific partial differential equations 3 Numerical methods for PDEs 4 …   Wikipedia

  • Nonlinear optics — (NLO) is the branch of optics that describes the behaviour of light in nonlinear media, that is, media in which the dielectric polarization P responds nonlinearly to the electric field E of the light. This nonlinearity is typically only observed… …   Wikipedia

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