  in theoretical physics, the (one-dimensional) nonlinear schrÃ¶dinger equation (nlse) is a nonlinear variation of the schrÃ¶dinger 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 generally, the nlse appears as one of universal equations that describe the evolution of slowly varying packets of quasi-monochromatic wave
Exactly_solvable_models Partial_differential_equations SchrAPdinger_equation