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1、REVIEWOFMODERNPHYSICS,VOLUME83,JANUARY–MARCH2011SolitonsinnonlinearlatticesYaroslavV.KartashovICFO-InstitutdeCienciesFotoniques,andUniversitatPolitecnicadeCatalunya,MediterraneanTechnologyPark,08860Castelldefels(Barcelona),SpainBorisA.MalomedDepartmentofPhysica
2、lElectronics,SchoolofElectricalEngineering,FacultyofEngineering,TelAvivUniversity,TelAviv,69978,IsraelLluisTornerICFO-InstitutdeCienciesFotoniques,andUniversitatPolitecnicadeCatalunya,MediterraneanTechnologyPark,08860Castelldefels(Barcelona),Spain(Received20Feb
3、ruary2010;published14April2011;publishererrorcorrected25April2011)Thisarticleoffersacomprehensivesurveyofresultsobtainedforsolitonsandcomplexnonlinearwavepatternssupportedbynonlinearlattices(NLs),whichrepresentaspatiallyperiodicmodu-lationofthelocalstrengthands
4、ignofthenonlinearity,andtheircombinationswithlinearlattices.Amajorityoftheresultsobtained,thusfar,inthisfieldandreviewedinthisarticlearetheoretical.Nevertheless,relevantexperimentalsettingsarealsosurveyed,withemphasisonperspectivesforimplementationofthetheoretic
5、alpredictionsintheexperiment.Physicalsystemsdiscussedinthereviewbelongtotherealmsofnonlinearoptics(includingartificialopticalmedia,suchasphotoniccrystals,andplasmonics)andBose-Einsteincondensation.Thesolitonsareconsideredinone,two,andthreedimensions.Basicpropert
6、iesofthesolitonspresentedinthereviewaretheirexistence,stability,andmobility.Althoughthefieldisstillfarfromcompletion,generalconclusionscanbedrawn.Inparticular,anovelfundamentalpropertyofone-dimensionalsolitons,whichdoesnotoccurintheabsenceofNLs,isafinitethreshold
7、valueofthesolitonnorm,necessaryfortheirexistence.Inmultidimensionalsettings,thestabilityofsolitonssupportedbythespatialmodulationofthenonlinearityisatrulychallengingproblem,fortheoreticalandexperimentalstudiesalike.Inboththeone-dimensionalandtwo-dimensionalcase
8、s,themechanismthatcreatessolitonsinNLsinprincipleisdifferentfromitscounterpartinlinearlattices,asthesolitonsarecreateddirectly,ratherthanbifurcatingfromBlochmodesoflinearlat
