Funded by he Deu sche Fo schungsgemeinscha (DFG) unde Ge many’s Excellence S a egy wi hin he Clus e o Excellence PhoenixD(EXC 2122, P ojec ID 390833453
Ge man Resea ch Founda ion
A ilia ions: (Ro isSans, blue, 36 p )
O. Melche , A. Demi can
Open-sou ce sol e s o soli on solu ions o nonlinea Sch ödinge - ype equa ions
Compu a ional p oblem sol ed by SW ools
Usage examples ho oughly documen ed unde Re . [1]
One-dimensional (1D) NSE So wa e in eg a ion wi h py- mas Two-dimensional (2D) NSE
Re e ences
Fu he ea u es
Leibniz Uni e si ä Hanno e , IQO, Wel enga en 1, 30167 Hanno e
Leibniz Uni e si ä Hanno e , PxD, Wel enga en 1A, 30167 Hanno e
*melche @iqo.uni-hanno e .de
We p esen open-sou ce Py hon ools o he nume ical calcula ion
o soli on solu ions o nonlinea Sch ödinge - ype equa ions in
nonlinea op ics and quan um mechanics. Two a ian s o he
co esponding nonlinea eigen alue p oblem (NEVP) a e
conside ed: a ba e NEVP, whe e a solu ion wi h p esc ibed
eigen alue is compu ed, and a cons ained NEVP, whe e a solu ion
wi h p esc ibed no m is compu ed. Linea s abili y o he
solu ions is assessed in he amewo k o soli on in e nal modes.
■ In eg a es well wi h py- mas [2] and GNLS ools.py [3]
■ Pic o ial ou line o SW ools [1]
■ 1D G oss-Pi ae skii equa ion ■ Highe -o de NSE [5] ■ 2D nonlinea Sch ödinge equa ion
■ NEVP wi h no maliza ion cons ain [1]
■ Usage example [1,4]
■ Usage example [1,7]
■ Ex endible so wa e amewo k
■ Tools o linea s abili y analysis
■ Lib a y o soli a y wa e examples
■ Gene alized nonlinea Sch ödinge equa ion (gene alized NSE)
■ Soli a y wa e ansa z
■ Nonlinea eigen alue p oblem (NEVP)
■ Conse a ion laws equi ed by he implemen ed algo i hms
■ Aim: ob ain soli a y wa e U by sui able i e a i e p ocedu e
p opaga ion coo dina e linea di e en ial ope a o
ans e se coo dina e nonlinea unc ional
complex- alued en elope
Funded by he Deu sche Fo schungsgemeinscha (DFG) unde Ge many’s Excellence S a egy wi hin he Clus e o Excellence PhoenixD (EXC 2122, P ojec ID 390833453).
Code: Compu e capsule: Pos e :
[1] O. Melche , A. Demi can, CPC 317 (2025) 109851
[2] O. Melche , A. Demi can, CPC 273 (2022) 108257
[3] O. Melche , A. Demi can, SFX 20 (2022) 101232
[4] W. Bao, Q. Du, SIAM 25 (2004) 1674
[5] O. Melche , A. Demi can, PRA 110 (2004) 043518
[7] J. Yang, Z. Musslimani, OL 28 (2003) 2094
[6] O. Sinkin e al., JLT 21 (2003) 61
• apping po en ial
• BEC wa e unc ion
• po en ial
• NEVP
• 2D ans e se ec o
• i e a i e solu ion me hod:
nonlinea successi e o e elaxa ion (NSOM)
• ini ial ial unc ion
• i e a i e solu ion me hod:
spec al eno maliza ion me hod (SRM)
• easy- o-use code in e ace
• (a) examples o soli a y wa e solu ions
• (b) e olu ion o he accu acy upon i e a ion
• in e ac ion pa ame e
he e:
■ So wa e in eg a ion [1,2]
• SW ools ``ba e'' NEVP sol e [1]
• pulse p opaga ion using py- mas [2]
(adap i e s epsize local e o me hod [6])
i e a e un il:
(accu acy)
