Nonlinear collective excitations and inhomogeneous states of the excitonic phase are examined with the interband transitions of pairing particles taken into account. We obtain a Ginzburg-Landau-like equation and find the necessary conditions for a second-order phase transition to take place. The nonlinear equation describing the excited (inhomogeneous) state of the system in a simple case appears to be the Sine-Gordon equation. It is shown that domains of magnetization or polarization appear in the excited state of the excitonic antiferromagnetic or antiferroelectric. There are also other excited states, where the charge density coexists with the magnetization density. The collective excitations are manifested as nonlinear magnetization or polarization waves, moving domains of magnetization, etc.
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Lozovik, Y.E., Klyuchnik, A.V. Current states and domains in systems with electron-hole pairing. J Low Temp Phys 38, 761–775 (1980). https://doi.org/10.1007/BF00115502
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DOI: https://doi.org/10.1007/BF00115502