Stability and dynamics of two-soliton molecules

U. Al Khawaja

Research output: Contribution to journalArticlepeer-review

39 Citations (Scopus)


The problem of soliton-soliton force is revisited. From the exact two-soliton solution of a nonautonomous Gross-Pitaevskii equation, we derive a generalized formula for the mutual force between two solitons. The force is given for arbitrary soliton amplitude difference, relative speed, phase, and separation. The latter allows for the investigation of soliton molecule formation, dynamics, and stability. We reveal the role of the time-dependent relative phase between the solitons in binding them in a soliton molecule. We derive its equilibrium bond length, spring constant, frequency, effective mass, and binding energy of the molecule. We investigate the molecule's stability against perturbations such as reflection from surfaces, scattering by barriers, and collisions with other solitons.

Original languageEnglish
Article number056603
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number5
Publication statusPublished - May 7 2010

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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