Interaction properties of the periodic and step-like solutions of the double-Sine-Gordon equation

  • Marzieh Peyravi
  • Afshin Montakhab
  • Nematollah Riazi
  • Abdorrasoul Gharaati
Statistical and Nonlinear Physics

Abstract

The periodic and step-like solutions of the double-Sine-Gordon equation are investigated, with different initial conditions and for various values of the potential parameter epsilon. We plot energy and force diagrams, as functions of the inter-soliton distance for such solutions. This allows us to consider our system as an interacting many-body system in 1+1 dimension. We therefore plot state diagrams (pressure vs. average density) for step-like as well as periodic solutions. Step-like solutions are shown to behave similarly to their counterparts in the Sine-Gordon system. However, periodic solutions show a fundamentally different behavior as the parameter epsilon is increased. We show that two distinct phases of periodic solutions exist which exhibit manifestly different behavior. Response functions for these phases are shown to behave differently, joining at an apparent phase transition point.

PACS

05.45.Yv Solitons 05.00.00 Statistical physics, thermodynamics, and nonlinear dynamical systems 02.60.Lj Ordinary and partial differential equations; boundary value problems 24.10.Jv Relativistic models 

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Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Marzieh Peyravi
    • 1
  • Afshin Montakhab
    • 2
  • Nematollah Riazi
    • 1
  • Abdorrasoul Gharaati
    • 3
  1. 1.Physics Department and Biruni ObservatoryShiraz UniversityShirazIran
  2. 2.Physics DepartmentShiraz UniversityShirazIran
  3. 3.Physics DepartmentPayame Noor UniversityShirazIran

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