New findings for the old problem: Exact solutions for domain walls in coupled real Ginzburg-Landau equations

@article{Malomed2021NewFF,
  title={New findings for the old problem: Exact solutions for domain walls in coupled real Ginzburg-Landau equations},
  author={Boris A. Malomed},
  journal={Physics Letters A},
  year={2021}
}
  • B. Malomed
  • Published 27 October 2021
  • Physics
  • Physics Letters A
2 Citations

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References

SHOWING 1-10 OF 59 REFERENCES
Domain Walls in the Coupled Gross–Pitaevskii Equations
A thorough study of domain wall solutions in coupled Gross–Pitaevskii equations on the real line is carried out including existence of these solutions; their spectral and nonlinear stability; their
Sources, sinks and wavenumber selection in coupled CGL equations and experimental implications for counter-propagating wave systems
We study the coupled complex Ginzburg–Landau (CGL) equations for traveling wave systems, and show that sources and sinks are the important coherent structures that organize much of the dynamical
Transition to miscibility in a binary Bose-Einstein condensate induced by linear coupling
A one-dimensional mean-field model of a two-component condensate in the parabolic trap is considered, with the components corresponding to different spin states of the same atom. We demonstrate that
Structure of binary Bose-Einstein condensates
We identify all possible classes of solutions for two-component Bose-Einstein condensates (BECs) within the Thomas-Fermi (TF) approximation and check these results against numerical simulations of
Amplitude equations from spatiotemporal binary-fluid convection data
We apply a recently developed method for the analysis of spatiotemporal data to extract the dynamical equations that describe an experiment on traveling-wave convection in a binary fluid. The
A Quasicrystallic Domain Wall in Nonlinear Dissipative Patterns
We propose an indirect approach to the generation of a two-dimensional quasiperiodic (QP) pattern in convection and similar nonlinear dissipative systems where a direct generation of stable uniform
Optical domain walls.
  • Malomed
  • Physics, Medicine
    Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 1994
TLDR
Dynamical properties of the domain walls (DW's) in the light beams propagating in nonlinear optical fibers are considered and a dark soliton in one core in the presence of the homogeneous field in the mate core is considered.
Stability and Grain Boundaries in the Dispersive Newell–Whitehead–Segel Equation
An equation to describe nearly 1D traveling-waves patterns, obtained first by Brand, Lomdahl and Newell, is revisited. In addition to the previously known transverse Benjamin–Feir condition,
The world of the complex Ginzburg-Landau equation
The cubic complex Ginzburg-Landau equation is one of the most-studied nonlinear equations in the physics community. It describes a vast variety of phenomena from nonlinear waves to second-order phase
Families of matter-waves in two-component Bose-Einstein condensates
Abstract.We produce several families of solutions for two-component nonlinear Schrödinger/Gross-Pitaevskii equations. These include domain walls and the first example of an antidark or gray soliton
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