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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 on the 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 responsible for energy transport along molecular chains; and many others. More gene

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rdfs:label	Equazione di Schrödinger non lineare (it) 非線形シュレディンガー方程式 (ja) Nonlinear Schrödinger equation (en) Нелинейное уравнение Шрёдингера (ru) Нелінійне рівняння Шредінгера (uk)
rdfs:comment	非線形シュレディンガー方程式（ひせんけいシュレディンガーほうていしき、英: Nonlinear Schrödinger equation）とは、を記述する偏微分方程式の一つ。英語表記を略してNLS方程式とも呼ばれる。方程式の形が一次元シュレディンガー方程式のポテンシャル項を非線形項で置き換えたものと等価であることから、この名前で呼ばれる。可積分系の代表的な例の一つであり、逆散乱法等の手法で解くことができる。一般的には分散性が強い波の非線形変調を記述しており、分散性の強い波動現象で包絡線が満たす方程式として普遍的に導かれる。一方で、ボーズ＝アインシュタイン凝縮におけるグロス＝ピタエフスキー方程式が三次元版の非線形シュレディンガー方程式に形式的に等価であるほか、渦糸の運動やスピンの歳差運動を記述する方程式から導くこともでき、波動現象を越えて、多彩な物理系に現れる。 (ja) Нелине́йное, или куби́ческое, уравне́ние Шрёдингера (НУШ) — нелинейное уравнение в частных производных второго порядка, играющее важную роль в теории нелинейных волн, в частности, в нелинейной оптике и физике плазмы. Уравнение имеет вид: где — комплекснозначная функция. (ru) Нелінійне або кубічне рівняння Шредінгера (НРШ, англ. Nonlinear Schrödinger equation (NLS)) — рівняння в частинних похідних другого порядку, що грає важливу роль в теорії , зокрема, в нелінійній оптиці і фізиці плазми. Є узагальненням лінійного , відомого в квантовій механіці як рівняння Шредінгера Рівняння має вигляд: де — комплекснозначна функція. (uk) 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 on the 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 responsible for energy transport along molecular chains; and many others. More gene (en) In fisica teorica l'equazione (unidimensionale) di Schrödinger non lineare (NLSE) è una variante non lineare dell'equazione di Schrödinger. È una equazione classica di campo le cui applicazioni principali sono nella propagazione della luce in fibre ottiche non lineari, in guide d'onda planari e in condensati di Bose-Einstein confinati (in trappole a forma di sigaro altamente anisotrope), in regime di campo medio. (it)
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dcterms:subject	Exactly solvable models Schrödinger equation Integrable systems Partial differential equations
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Link from a Wikipage to another Wikipage	Quantum field theory Quantum mechanics Rogue wave Schrödinger equation Elevation Modulation Bethe ansatz Vladimir E. Zakharov Davydov soliton Inverse scattering transform Lieb–Liniger model Tonks–Girardeau gas Complex number Crank–Nicolson method Normal order Wavenumber Classical field theory Classical mechanics Envelope (mathematics) Gravity waves Exactly solvable models Complex conjugate Schrödinger equation Hamiltonian (quantum mechanics) Dark soliton Phase (waves) Theoretical physics Dispersion relation Galilean invariance Landau–Lifshitz model Logarithmic Schrödinger equation Amplitude Curvature Earth's gravity Angular velocity Breather Four-wave mixing Ishimori equation Jordan–Wigner transformation Group velocity Hamiltonian mechanics AKNS system Integrable systems Partial differential equations Eckhaus equation Heisenberg ferromagnet Dispersion (water waves) Bose–Einstein condensate Poisson bracket Spectral method Gross–Pitaevskii equation Dispersion (optics) Carrier wave Raman scattering Manakov system Second-harmonic generation Self-phase modulation Schrödinger field Soliton Soliton (optics) Yang Chen-Ning Dimensionless Optics Ultrashort pulse Quartic interaction Nonlinear partial differential equation Canonical quantization Spin–statistics theorem

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