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Nonlinear Schrödinger equation

Index Nonlinear Schrödinger equation

In theoretical physics, the (one-dimensional) nonlinear Schrödinger equation (NLSE) is a nonlinear variation of the Schrödinger equation. [1]

69 relations: AKNS system, Amplitude, Angular frequency, Bethe ansatz, Bose–Einstein condensate, Breather, Carrier wave, Chen-Ning Yang, Classical field theory, Classical mechanics, Complex conjugate, Complex number, Curvature, Davydov soliton, Dimensionless quantity, Dispersion (water waves), Dispersion relation, Eckhaus equation, Elevation, Envelope (mathematics), Four-wave mixing, Galilean invariance, Ginzburg–Landau theory, Gravity of Earth, Gravity wave, Gross–Pitaevskii equation, Group velocity, Group velocity dispersion, Hamiltonian (quantum mechanics), Hamiltonian mechanics, Integrable system, Inverse scattering transform, Ishimori equation, John Scott Russell, Jordan–Wigner transformation, Landau–Lifshitz model, Lieb–Liniger model, Logarithmic Schrödinger equation, Manakov system, Modified Morlet wavelet, Modulation, Nonlinear partial differential equation, Normal order, Optics, Phase (waves), Plasma oscillation, Poisson bracket, Quantum field theory, Quantum mechanics, Quartic interaction, ..., Raman scattering, Rogue wave, Schrödinger equation, Schrödinger field, Second quantization, Second-harmonic generation, Self-phase modulation, Soliton, Soliton (optics), Spin wave, Spin–statistics theorem, Split-step method, Theoretical physics, Tonks–Girardeau gas, Ultrashort pulse, Vladimir E. Zakharov, Wavelength, Wavenumber, Wind wave. Expand index (19 more) »

AKNS system

In mathematics, the AKNS system is an integrable system of partial differential equations, introduced by and named after.

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Amplitude

The amplitude of a periodic variable is a measure of its change over a single period (such as time or spatial period).

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Angular frequency

In physics, angular frequency ω (also referred to by the terms angular speed, radial frequency, circular frequency, orbital frequency, radian frequency, and pulsatance) is a scalar measure of rotation rate.

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Bethe ansatz

In physics, the Bethe ansatz is an ansatz method for finding the exact solutions of certain one-dimensional quantum many-body models.

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Bose–Einstein condensate

A Bose–Einstein condensate (BEC) is a state of matter of a dilute gas of bosons cooled to temperatures very close to absolute zero.

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Breather

In physics, a breather is a nonlinear wave in which energy concentrates in a localized and oscillatory fashion.

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Carrier wave

In telecommunications, a carrier wave, carrier signal, or just carrier, is a waveform (usually sinusoidal) that is modulated (modified) with an input signal for the purpose of conveying information.

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Chen-Ning Yang

Chen-Ning Yang or Yang Zhenning (born October 1, 1922) is a Chinese physicist who works on statistical mechanics and particle physics.

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Classical field theory

A classical field theory is a physical theory that predicts how one or more physical fields interact with matter through field equations.

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Classical mechanics

Classical mechanics describes the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars and galaxies.

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Complex conjugate

In mathematics, the complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign.

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Complex number

A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.

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Curvature

In mathematics, curvature is any of a number of loosely related concepts in different areas of geometry.

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Davydov soliton

Davydov soliton is a quantum quasiparticle representing an excitation propagating along the protein α-helix self-trapped amide I. It is a solution of the Davydov Hamiltonian.

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Dimensionless quantity

In dimensional analysis, a dimensionless quantity is a quantity to which no physical dimension is assigned.

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Dispersion (water waves)

In fluid dynamics, dispersion of water waves generally refers to frequency dispersion, which means that waves of different wavelengths travel at different phase speeds.

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Dispersion relation

In physical sciences and electrical engineering, dispersion relations describe the effect of dispersion in a medium on the properties of a wave traveling within that medium.

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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.

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Elevation

The elevation of a geographic location is its height above or below a fixed reference point, most commonly a reference geoid, a mathematical model of the Earth's sea level as an equipotential gravitational surface (see Geodetic datum § Vertical datum).

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Envelope (mathematics)

In geometry, an envelope of a family of curves in the plane is a curve that is tangent to each member of the family at some point, and these points of tangency together form the whole envelope.

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Four-wave mixing

Four-wave mixing (FWM) is an intermodulation phenomenon in non-linear optics, whereby interactions between two or three wavelengths produce two or one new wavelengths.

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Galilean invariance

Galilean invariance or Galilean relativity states that the laws of motion are the same in all inertial frames.

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Ginzburg–Landau theory

In physics, Ginzburg–Landau theory, often called Landau–Ginzburg theory, named after Vitaly Lazarevich Ginzburg and Lev Landau, is a mathematical physical theory used to describe superconductivity.

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Gravity of Earth

The gravity of Earth, which is denoted by, refers to the acceleration that is imparted to objects due to the distribution of mass within Earth.

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Gravity wave

In fluid dynamics, gravity waves are waves generated in a fluid medium or at the interface between two media when the force of gravity or buoyancy tries to restore equilibrium.

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Gross–Pitaevskii equation

The Gross–Pitaevskii equation (GPE, named after Eugene P. Gross and Lev Petrovich Pitaevskii) describes the ground state of a quantum system of identical bosons using the Hartree–Fock approximation and the pseudopotential interaction model.

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Group velocity

The group velocity of a wave is the velocity with which the overall shape of the wave's amplitudes—known as the modulation or envelope of the wave—propagates through space.

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Group velocity dispersion

In optics, group velocity dispersion (GVD) is a characteristic of a dispersive medium, used most often to determine how the medium will affect the duration of an optical pulse traveling through it.

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Hamiltonian (quantum mechanics)

In quantum mechanics, a Hamiltonian is an operator corresponding to the total energy of the system in most of the cases.

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Hamiltonian mechanics

Hamiltonian mechanics is a theory developed as a reformulation of classical mechanics and predicts the same outcomes as non-Hamiltonian classical mechanics.

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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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Inverse scattering transform

In mathematics, the inverse scattering transform is a method for solving some non-linear partial differential equations.

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Ishimori equation

The Ishimori equation (IE) is a partial differential equation proposed by the Japanese mathematician.

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John Scott Russell

John Scott Russell FRSE FRS (9 May 1808, Parkhead, Glasgow – 8 June 1882, Ventnor, Isle of Wight) was a Scottish civil engineer, naval architect and shipbuilder who built the Great Eastern in collaboration with Isambard Kingdom Brunel.

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Jordan–Wigner transformation

The Jordan–Wigner transformation is a transformation that maps spin operators onto fermionic creation and annihilation operators.

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Landau–Lifshitz model

In solid-state physics, the Landau–Lifshitz equation (LLE), named for Lev Landau and Evgeny Lifshitz, is a partial differential equation describing time evolution of magnetism in solids, depending on 1 time variable and 1, 2, or 3 space variables.

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Lieb–Liniger model

The Lieb–Liniger model describes a gas of particles moving in one dimension and satisfying Bose–Einstein statistics.

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Logarithmic Schrödinger equation

In theoretical physics, the logarithmic Schrödinger equation (sometimes abbreviated as LNSE or LogSE) is one of the nonlinear modifications of Schrödinger's equation.

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Manakov system

Maxwell's Equations, when converted to cylindrical coordinates, and with the boundary conditions for an optical fiber while including birefringence as an effect taken into account, will yield the coupled nonlinear Schrödinger equations.

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Modified Morlet wavelet

Modified Mexican hat, Modified Morlet and Dark soliton or Darklet wavelets are derived from hyperbolic (sech) (bright soliton) and hyperbolic tangent (tanh) (dark soliton) pulses.

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Modulation

In electronics and telecommunications, modulation is the process of varying one or more properties of a periodic waveform, called the carrier signal, with a modulating signal that typically contains information to be transmitted.

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Nonlinear partial differential equation

In mathematics and physics, a nonlinear partial differential equation is a partial differential equation with nonlinear terms.

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Normal order

In quantum field theory a product of quantum fields, or equivalently their creation and annihilation operators, is usually said to be normal ordered (also called Wick order) when all creation operators are to the left of all annihilation operators in the product.

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Optics

Optics is the branch of physics which involves the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it.

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Phase (waves)

Phase is the position of a point in time (an instant) on a waveform cycle.

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Plasma oscillation

Plasma oscillations, also known as Langmuir waves (after Irving Langmuir), are rapid oscillations of the electron density in conducting media such as plasmas or metals in the ultraviolet region.

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Poisson bracket

In mathematics and classical mechanics, the Poisson bracket is an important binary operation in Hamiltonian mechanics, playing a central role in Hamilton's equations of motion, which govern the time evolution of a Hamiltonian dynamical system.

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Quantum field theory

In theoretical physics, quantum field theory (QFT) is the theoretical framework for constructing quantum mechanical models of subatomic particles in particle physics and quasiparticles in condensed matter physics.

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Quantum mechanics

Quantum mechanics (QM; also known as quantum physics, quantum theory, the wave mechanical model, or matrix mechanics), including quantum field theory, is a fundamental theory in physics which describes nature at the smallest scales of energy levels of atoms and subatomic particles.

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Quartic interaction

In quantum field theory, a quartic interaction is a type of self-interaction in a scalar field.

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Raman scattering

Raman scattering or the Raman effect is the inelastic scattering of a photon by molecules which are excited to higher vibrational or rotational energy levels.

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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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Schrödinger field

In quantum mechanics and quantum field theory, a Schrödinger field, named after Erwin Schrödinger, is a quantum field which obeys the Schrödinger equation.

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Second quantization

Second quantization, also referred to as occupation number representation, is a formalism used to describe and analyze quantum many-body systems.

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Second-harmonic generation

Second harmonic generation (also called frequency doubling or SHG) is a nonlinear optical process in which two photons with the same frequency interact with a nonlinear material, are "combined", and generate a new photon with twice the energy of the initial photons (equivalently, twice the frequency and half the wavelength).

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Self-phase modulation

Self-phase modulation (SPM) is a nonlinear optical effect of light-matter interaction.

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Soliton

In mathematics and physics, a soliton is a self-reinforcing solitary wave packet that maintains its shape while it propagates at a constant velocity.

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Soliton (optics)

In optics, the term soliton is used to refer to any optical field that does not change during propagation because of a delicate balance between nonlinear and linear effects in the medium.

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Spin wave

Spin waves are propagating disturbances in the ordering of magnetic materials.

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Spin–statistics theorem

In quantum mechanics, the spin–statistics theorem relates the intrinsic spin of a particle (angular momentum not due to the orbital motion) to the particle statistics it obeys.

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Split-step method

In numerical analysis, the split-step (Fourier) method is a pseudo-spectral numerical method used to solve nonlinear partial differential equations like the nonlinear Schrödinger equation.

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Theoretical physics

Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena.

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Tonks–Girardeau gas

In physics, a Tonks–Girardeau gas is a Bose gas in which the repulsive interactions between bosonic particles confined to one dimension dominate the physics of the system.

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Ultrashort pulse

In optics, an ultrashort pulse of light is an electromagnetic pulse whose time duration is of the order of a picosecond (10−12 second) or less.

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Vladimir E. Zakharov

Vladimir Evgen'evich Zakharov (Влади́мир Евге́ньевич Заха́ров; born August 1, 1939) is a Soviet and Russian mathematician and physicist.

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Wavelength

In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats.

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Wavenumber

In the physical sciences, the wavenumber (also wave number or repetency) is the spatial frequency of a wave, measured in cycles per unit distance or radians per unit distance.

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Wind wave

In fluid dynamics, wind waves, or wind-generated waves, are surface waves that occur on the free surface of bodies of water (like oceans, seas, lakes, rivers, canals, puddles or ponds).

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References

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

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