Nonlinear Schrödinger equation

URI: https://gptkb.org/entity/Nonlinear_Schrödinger_equation

GPTKB entity

Statements (48)

Predicate	Object
gptkbp:instanceOf	partial differential equations
gptkbp:describes	evolution of complex wave amplitude
gptkbp:field	gptkb:nonlinear_optics fluid dynamics mathematical physics quantum mechanics
gptkbp:formulated_in	1970s
gptkbp:generalizes	gptkb:linear_Schrödinger_equation
gptkbp:has_mathematical_property	conservation of energy conservation of momentum conservation of norm
gptkbp:has_solution_type	soliton breather rogue wave
gptkbp:hasApplication	modeling deep water waves modeling plasma waves modeling pulse propagation in optical fibers modeling superfluids
gptkbp:hasModel	nonlinear wave propagation self-focusing envelope solitons modulational instability self-phase modulation
gptkbp:hasVariant	gptkb:Gross–Pitaevskii_equation gptkb:Manakov_system gptkb:cubic-quintic_nonlinear_Schrödinger_equation gptkb:derivative_nonlinear_Schrödinger_equation
https://www.w3.org/2000/01/rdf-schema#label	Nonlinear Schrödinger equation
gptkbp:is_integrable	in 1D with cubic nonlinearity
gptkbp:namedAfter	gptkb:Erwin_Schrödinger
gptkbp:parameter	dispersion coefficient nonlinearity coefficient
gptkbp:relatedTo	gptkb:Korteweg–de_Vries_equation gptkb:sine-Gordon_equation gptkb:Zakharov–Shabat_system integrable systems inverse scattering transform
gptkbp:studiedBy	gptkb:theoretical_physics applied mathematics engineering
gptkbp:symmetry	gptkb:Galilean_invariance phase invariance scaling invariance
gptkbp:used_in	gptkb:Bose-Einstein_condensates fiber optics water waves
gptkbp:bfsParent	gptkb:Korteweg–de_Vries_equation
gptkbp:bfsLayer	5