Layered solutions for a nonlocal Ginzburg-Landau model with periodic modulation

Ko Shin Chen, Cyrill Muratov, Xiaodong Yan

Research output: Contribution to journalArticlepeer-review


We study layered solutions in a one-dimensional version of the scalar Ginzburg-Landau equation that involves a mixture of a second spatial derivative and a fractional half-derivative, together with a periodically modulated nonlinearity. This equation appears as the Euler-Lagrange equation of a suitably renormalized fractional Ginzburg-Landau energy with a double-well potential that is multiplied by a 1-periodically varying nonnegative factor g(x) with (Formula presented). A priori this energy is not bounded below due to the presence of a nonlocal term in the energy. Nevertheless, through a careful analysis of a minimizing sequence we prove existence of global energy minimizers that connect the two wells at infinity. These minimizers are shown to be the classical solutions of the associated nonlocal Ginzburg-Landau type equation.

Original languageEnglish (US)
JournalMathematics In Engineering
Issue number5
StatePublished - 2023

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematical Physics
  • Applied Mathematics


  • layered solutions
  • nonlocal Ginzburg-Landau
  • periodic modulation


Dive into the research topics of 'Layered solutions for a nonlocal Ginzburg-Landau model with periodic modulation'. Together they form a unique fingerprint.

Cite this