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• Nonlinear_Schrödinger_equation abstract "In theoretical physics, the (one-dimensional) nonlinear Schrödinger equation (NLSE) is a nonlinear variation of the Schrödinger equation. It is a classical field equation whose principal applications are to the propagation of light in nonlinear optical fibers and planar waveguides and to Bose-Einstein condensates confined to highly anisotropic cigar-shaped traps, in the mean-field regime. Additionally, the equation appears in the studies of small-amplitude gravity waves onthe surface of deep inviscid (zero-viscosity) water; the Langmuir waves in hot plasmas; the propagation of plane-diffracted wave beams in the focusing regions of the ionosphere; the propagation of Davydov's alpha-helix solitons, which are responsiblefor energy transport along molecular chains; and many others. More generally, the NLSE appears as one of universal equations that describe the evolution of slowly varying packetsof quasi-monochromatic waves in weakly nonlinear media that have dispersion. Unlike the linear Schrödinger equation, the NLSE never describes the time evolution of a quantum state (except hypothetically, as in some early attempts, in the 1970s, to explain the quantum measurement process). The 1D NLSE is an example of an integrable model.In quantum mechanics, the 1D NLSE is a special case of the classical nonlinear Schrödinger field, which in turn is a classical limit of a quantum Schrödinger field. Conversely, when the classical Schrödinger field is canonically quantized, it becomes a quantum field theory (which is linear, despite the fact that it is called ″quantum nonlinear Schrödinger equation″) that describes bosonic point particles with delta-function interactions — the particles either repel or attract when they are at the same point. In fact, when the number of particles is finite, this quantum field theory is equivalent to the Lieb–Liniger model. Both the quantum and the classical 1D nonlinear Schrödinger equations are integrable. Of special interest is the limit of infinite strength repulsion, in which case the Lieb–Liniger model becomes the Tonks–Girardeau gas (also called the hard-core Bose gas, or impenetrable Bose gas). In this limit, the bosons may, by a change of variables that is a continuum generalization of the Jordan–Wigner transformation, be transformed to a system one-dimensional noninteracting spinless fermions.The nonlinear Schrödinger equation is a simplified 1+1-dimensional form of the Ginzburg–Landau equation introduced in 1950 in their work on superconductivity, and was written down explicitly by R. Y. Chiao, E. Garmire, and C. H. Townes (1964, equation (5)) in their study of optical beams.Multi-dimensional version replaces the second spatial derivative by the Laplacian. In more than one dimension, the equation is not integrable, it allows for a collapse and wave turbulence".
• Nonlinear_Schrödinger_equation thumbnail NLS_breathers_-_Akhmediev_Peregrine_and_Kuznetsov-Ma_breather.jpg?width=300.
• Nonlinear_Schrödinger_equation wikiPageExternalLink npde1401.pdf.
• Nonlinear_Schrödinger_equation wikiPageExternalLink npde1402.pdf.
• Nonlinear_Schrödinger_equation wikiPageExternalLink npde1403.pdf.
• Nonlinear_Schrödinger_equation wikiPageExternalLink davis.pdf.
• Nonlinear_Schrödinger_equation wikiPageExternalLink falkovich.
• Nonlinear_Schrödinger_equation wikiPageExternalLink NLS.
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• Nonlinear_Schrödinger_equation wikiPageWikiLink AKNS_system.
• Nonlinear_Schrödinger_equation wikiPageWikiLink Amplitude.
• Nonlinear_Schrödinger_equation wikiPageWikiLink Angular_frequency.
• Nonlinear_Schrödinger_equation wikiPageWikiLink Bethe_ansatz.
• Nonlinear_Schrödinger_equation wikiPageWikiLink Bose–Einstein_condensate.
• Nonlinear_Schrödinger_equation wikiPageWikiLink Breather.
• Nonlinear_Schrödinger_equation wikiPageWikiLink Bright_soliton.
• Nonlinear_Schrödinger_equation wikiPageWikiLink Carrier_wave.
• Nonlinear_Schrödinger_equation wikiPageWikiLink Category:Exactly_solvable_models.
• Nonlinear_Schrödinger_equation wikiPageWikiLink Category:Partial_differential_equations.
• Nonlinear_Schrödinger_equation wikiPageWikiLink Category:Schrödinger_equation.
• Nonlinear_Schrödinger_equation wikiPageWikiLink Chen-Ning_Yang.
• Nonlinear_Schrödinger_equation wikiPageWikiLink Classical_field_theory.
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• Nonlinear_Schrödinger_equation wikiPageWikiLink Darboux_transformation.
• Nonlinear_Schrödinger_equation wikiPageWikiLink Dark_soliton.
• Nonlinear_Schrödinger_equation wikiPageWikiLink Davydov_soliton.
• Nonlinear_Schrödinger_equation wikiPageWikiLink Dimensionless_quantity.
• Nonlinear_Schrödinger_equation wikiPageWikiLink Dispersion_(water_waves).
• Nonlinear_Schrödinger_equation wikiPageWikiLink Dispersion_relation.
• Nonlinear_Schrödinger_equation wikiPageWikiLink Eckhaus_equation.
• Nonlinear_Schrödinger_equation wikiPageWikiLink Elevation.
• Nonlinear_Schrödinger_equation wikiPageWikiLink Envelope_(mathematics).
• Nonlinear_Schrödinger_equation wikiPageWikiLink Four-wave_mixing.
• Nonlinear_Schrödinger_equation wikiPageWikiLink Galilean_invariance.
• Nonlinear_Schrödinger_equation wikiPageWikiLink Ginzburg–Landau_theory.
• Nonlinear_Schrödinger_equation wikiPageWikiLink Gravity_of_Earth.
• Nonlinear_Schrödinger_equation wikiPageWikiLink Gravity_wave.
• Nonlinear_Schrödinger_equation wikiPageWikiLink Gross–Pitaevskii_equation.
• Nonlinear_Schrödinger_equation wikiPageWikiLink Group_velocity.
• Nonlinear_Schrödinger_equation wikiPageWikiLink Hamiltonian_(quantum_mechanics).
• Nonlinear_Schrödinger_equation wikiPageWikiLink Hamiltonian_mechanics.
• Nonlinear_Schrödinger_equation wikiPageWikiLink Integrable_system.
• Nonlinear_Schrödinger_equation wikiPageWikiLink Inverse_scattering_transform.
• Nonlinear_Schrödinger_equation wikiPageWikiLink Ishimori_equation.
• Nonlinear_Schrödinger_equation wikiPageWikiLink John_Scott_Russell.
• Nonlinear_Schrödinger_equation wikiPageWikiLink Jordan–Wigner_transformation.
• Nonlinear_Schrödinger_equation wikiPageWikiLink Landau–Lifshitz_model.
• Nonlinear_Schrödinger_equation wikiPageWikiLink Lieb–Liniger_model.
• Nonlinear_Schrödinger_equation wikiPageWikiLink List_of_nonlinear_partial_differential_equations.
• Nonlinear_Schrödinger_equation wikiPageWikiLink Manakov_system.
• Nonlinear_Schrödinger_equation wikiPageWikiLink Modulation.
• Nonlinear_Schrödinger_equation wikiPageWikiLink Normal_order.
• Nonlinear_Schrödinger_equation wikiPageWikiLink Optics.
• Nonlinear_Schrödinger_equation wikiPageWikiLink Phase_(waves).
• Nonlinear_Schrödinger_equation wikiPageWikiLink Plasma_oscillation.
• Nonlinear_Schrödinger_equation wikiPageWikiLink Poisson_bracket.
• Nonlinear_Schrödinger_equation wikiPageWikiLink Quantum_field_theory.
• Nonlinear_Schrödinger_equation wikiPageWikiLink Quantum_mechanics.
• Nonlinear_Schrödinger_equation wikiPageWikiLink Quartic_interaction.
• Nonlinear_Schrödinger_equation wikiPageWikiLink Raman_scattering.
• Nonlinear_Schrödinger_equation wikiPageWikiLink Rogue_wave.
• Nonlinear_Schrödinger_equation wikiPageWikiLink Schrödinger_equation.
• Nonlinear_Schrödinger_equation wikiPageWikiLink Schrödinger_field.
• Nonlinear_Schrödinger_equation wikiPageWikiLink Second-harmonic_generation.
• Nonlinear_Schrödinger_equation wikiPageWikiLink Second_quantization.
• Nonlinear_Schrödinger_equation wikiPageWikiLink Self-phase_modulation.
• Nonlinear_Schrödinger_equation wikiPageWikiLink Soliton.
• Nonlinear_Schrödinger_equation wikiPageWikiLink Soliton_(optics).
• Nonlinear_Schrödinger_equation wikiPageWikiLink Spin_wave.
• Nonlinear_Schrödinger_equation wikiPageWikiLink Spin–statistics_theorem.
• Nonlinear_Schrödinger_equation wikiPageWikiLink Split-step_method.
• Nonlinear_Schrödinger_equation wikiPageWikiLink Theoretical_physics.
• Nonlinear_Schrödinger_equation wikiPageWikiLink Tonks–Girardeau_gas.
• Nonlinear_Schrödinger_equation wikiPageWikiLink Vladimir_E._Zakharov.
• Nonlinear_Schrödinger_equation wikiPageWikiLink Wavelength.
• Nonlinear_Schrödinger_equation wikiPageWikiLink Wavenumber.
• Nonlinear_Schrödinger_equation wikiPageWikiLink Wind_wave.
• Nonlinear_Schrödinger_equation wikiPageWikiLink Zakharov–Shabat_system.
• Nonlinear_Schrödinger_equation wikiPageWikiLink File:NLS_breathers_-_Akhmediev_Peregrine_and_Kuznetsov-Ma_breather.jpg.
• Nonlinear_Schrödinger_equation wikiPageWikiLink File:Sech_soliton.svg.
• Nonlinear_Schrödinger_equation wikiPageWikiLinkText "Nonlinear Schrödinger (cubic)".
• Nonlinear_Schrödinger_equation wikiPageWikiLinkText "Nonlinear Schrödinger (derivative)".
• Nonlinear_Schrödinger_equation wikiPageWikiLinkText "Nonlinear Schrödinger equation ".
• Nonlinear_Schrödinger_equation wikiPageWikiLinkText "Nonlinear Schrödinger equation".
• Nonlinear_Schrödinger_equation wikiPageWikiLinkText "nonlinear Schrödinger equation".
• Nonlinear_Schrödinger_equation wikiPageWikiLinkText "nonlinear Schrödinger".
• Nonlinear_Schrödinger_equation wikiPageWikiLinkText "nonlinear".
• Nonlinear_Schrödinger_equation first "C. H.".
• Nonlinear_Schrödinger_equation first "E.".
• Nonlinear_Schrödinger_equation first "R. Y.".
• Nonlinear_Schrödinger_equation last "Chiao".
• Nonlinear_Schrödinger_equation last "Garmire".
• Nonlinear_Schrödinger_equation last "Townes".
• Nonlinear_Schrödinger_equation loc "equation".
• Nonlinear_Schrödinger_equation title "Nonlinear Schrodinger systems".

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