Unlike the linear Schrödinger equation, the NLSE never describes the time evolution of a quantum state. Of quasi-monochromatic waves in weakly nonlinear media that have dispersion. More generally, the NLSE appears as one of universal equations that describe the evolution of slowly varying packets 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. 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. In theoretical physics, the (one-dimensional) nonlinear Schrödinger equation ( NLSE) is a nonlinear variation of the Schrödinger equation. (A) The Akhmediev breather (B) the Peregrine breather (C) the Kuznetsov–Ma breather. Absolute value of the complex envelope of exact analytical breather solutions of the nonlinear Schrödinger (NLS) equation in nondimensional form. For the equation used in Bose–Einstein condensate theory, see Gross–Pitaevskii equation.
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