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Eckhaus equation

Index Eckhaus equation

In mathematical physics, the Eckhaus equation – or the Kundu–Eckhaus equation – is a nonlinear partial differential equations within the nonlinear Schrödinger class: The equation was independently introduced by Wiktor Eckhaus and by Anjan Kundu to model the propagation of waves in dispersive media. [1]

10 relations: Dispersion (optics), Integrable system, Linearization, Mathematical physics, Nonlinear Schrödinger equation, Partial differential equation, Rogue wave, Schrödinger equation, Wave, Wiktor Eckhaus.

Dispersion (optics)

In optics, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency.

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Integrable system

In the context of differential equations to integrate an equation means to solve it from initial conditions.

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Linearization

In mathematics, linearization is finding the linear approximation to a function at a given point.

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Mathematical physics

Mathematical physics refers to the development of mathematical methods for application to problems in physics.

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Nonlinear Schrödinger equation

In theoretical physics, the (one-dimensional) nonlinear Schrödinger equation (NLSE) is a nonlinear variation of the Schrödinger equation.

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Partial differential equation

In mathematics, a partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives.

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Rogue wave

Rogue waves (also known as freak waves, monster waves, episodic waves, killer waves, extreme waves, and abnormal waves) are large, unexpected and suddenly appearing surface waves that can be extremely dangerous, even to large ships such as ocean liners.

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Schrödinger equation

In quantum mechanics, the Schrödinger equation is a mathematical equation that describes the changes over time of a physical system in which quantum effects, such as wave–particle duality, are significant.

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Wave

In physics, a wave is a disturbance that transfers energy through matter or space, with little or no associated mass transport.

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Wiktor Eckhaus

Wiktor Eckhaus (28 June 1930 – 1 October 2000) was a Polish–Dutch mathematician, known for his work on the field of differential equations.

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Redirects here:

Kundu-Eckhaus equation, Kundu–Eckhaus equation.

References

[1] https://en.wikipedia.org/wiki/Eckhaus_equation

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