Communications in Mathematical Physics

, Volume 302, Issue 3, pp 815–841 | Cite as

Breather Solutions in Periodic Media

  • Carsten Blank
  • Martina Chirilus-Bruckner
  • Vincent Lescarret
  • Guido SchneiderEmail author


For nonlinear wave equations existence proofs for breathers are very rare. In the spatially homogeneous case up to rescaling the sine-Gordon equation \({\partial^2_t u = \partial^2_x u - \sin (u)}\) is the only nonlinear wave equation which is known to possess breather solutions. For nonlinear wave equations in periodic media no examples of breather solutions have been known so far. Using spatial dynamics, center manifold theory and bifurcation theory for periodic systems we construct for the first time such time periodic solutions of finite energy for a nonlinear wave equation
$$ s(x) \partial^2_t u(x,t) = \partial^2_x u(x,t) - q(x) u(x,t)+ r(x)u(x,t)^3, $$
with spatially periodic coefficients s, q, and r on the real axis. Such breather solutions play an important role in theoretical scenarios where photonic crystals are used as optical storage.


Photonic Crystal Homoclinic Orbit Stable Manifold Center Manifold Nonlinear Wave Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Carsten Blank
    • 1
  • Martina Chirilus-Bruckner
    • 1
  • Vincent Lescarret
    • 1
  • Guido Schneider
    • 1
    Email author
  1. 1.Institut für Analysis, Dynamik und ModellierungUniversität StuttgartStuttgartGermany

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