TY - JOUR

T1 - Interaction of dissipative solitons stabilized by nonlinear gradient terms

AU - Descalzi, Orazio

AU - Cartés, Carlos Gabriel

AU - Brand, Helmut R.

N1 - Funding Information:
O.D. and C.C. wish to acknowledge the support of FONDECYT (CL), Grant No. 1200357 and Universidad de los Andes through FAI initiatives. H.R.B. thanks the Deutsche Forschungsgemeinschaft (DE) for partial support of this work.
Publisher Copyright:
© 2021 American Physical Society.

PY - 2021/4/1

Y1 - 2021/4/1

N2 - We study the interaction of stable dissipative solitons of the cubic complex Ginzburg-Landau equation which are stabilized only by nonlinear gradient terms. In this paper we focus for the interactions in particular on the influence of the nonlinear gradient term associated with the Raman effect. Depending on its magnitude, we find up to seven possible outcomes of theses collisions: Stationary bound states, oscillatory bound states, meandering oscillatory bound states, bound states with large-amplitude oscillations, partial annihilation, complete annihilation, and interpenetration. Detailed results and their analysis are presented for one value of the corresponding nonlinear gradient term, while the results for two other values are just mentioned briefly. We compare our results with those obtained for coupled cubic-quintic complex Ginzburg-Landau equations and with the cubic-quintic complex Swift-Hohenberg equation. It turns out that both meandering oscillatory bound states as well as bound states with large-amplitude oscillations appear to be specific for coupled cubic complex Ginzburg-Landau equations with a stabilizing cubic nonlinear gradient term. Remarkably, we find for the large-amplitude oscillations a linear relationship between oscillation amplitude and period.

AB - We study the interaction of stable dissipative solitons of the cubic complex Ginzburg-Landau equation which are stabilized only by nonlinear gradient terms. In this paper we focus for the interactions in particular on the influence of the nonlinear gradient term associated with the Raman effect. Depending on its magnitude, we find up to seven possible outcomes of theses collisions: Stationary bound states, oscillatory bound states, meandering oscillatory bound states, bound states with large-amplitude oscillations, partial annihilation, complete annihilation, and interpenetration. Detailed results and their analysis are presented for one value of the corresponding nonlinear gradient term, while the results for two other values are just mentioned briefly. We compare our results with those obtained for coupled cubic-quintic complex Ginzburg-Landau equations and with the cubic-quintic complex Swift-Hohenberg equation. It turns out that both meandering oscillatory bound states as well as bound states with large-amplitude oscillations appear to be specific for coupled cubic complex Ginzburg-Landau equations with a stabilizing cubic nonlinear gradient term. Remarkably, we find for the large-amplitude oscillations a linear relationship between oscillation amplitude and period.

KW - Ginzburg-Landau equation

KW - Oscillations

UR - http://www.scopus.com/inward/record.url?scp=85105395015&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.103.042215

DO - 10.1103/PhysRevE.103.042215

M3 - Article

AN - SCOPUS:85105395015

VL - 103

JO - Physical Review E

JF - Physical Review E

SN - 2470-0045

IS - 4

M1 - 042215

ER -