Soliton and breather splitting on star graphs from tricrystal Josephson junctions

Hadi Susanto, Natanael Karjanto, Zulkarnain, Toto Nusantara, Taufiq Widjanarko

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


We consider the interactions of traveling localized wave solutions with a vertex in a star graph domain that describes multiple Josephson junctions with a common/branch point (i.e., tricrystal junctions). The system is modeled by the sine-Gordon equation. The vertex is represented by boundary conditions that are determined by the continuity of the magnetic field and vanishing total fluxes. When one considers small-amplitude breather solutions, the system can be reduced into the nonlinear Schrödinger equation posed on a star graph. Using the equation, we show that a high-velocity incoming soliton is split into a transmitted component and a reflected one. The transmission is shown to be in good agreement with the transmission rate of plane waves in the linear Schrödinger equation on the same graph (i.e., a quantum graph). In the context of the sine-Gordon equation, small-amplitude breathers show similar qualitative behaviors, while large-amplitude ones produce complex dynamics.

Original languageBritish English
Article number271
Issue number2
StatePublished - 1 Feb 2019


  • Breather
  • Quantum graph
  • Schrödinger equation
  • Sine-Gordon equation
  • Soliton
  • Star graph


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