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Nonlinear amplification of coherent waves in media with soliton-type refractive index pattern
Conte Robert, Bugaychuk Svetlana
We derive the complex Ginzburg-Landau equation for the dynamical self-diffraction of optical waves in a nonlinear cavity. The case of the reflection geometry of wave interaction as…
Meromorphic traveling wave solutions of the complex cubic-quintic Ginzburg-Landau equation
Robert Conte, Tuen-Wai Ng
We look for singlevalued solutions of the squared modulus M of the traveling wave reduction of the complex cubic-quintic Ginzburg-Landau equation. Using Clunie's lemma, we first pr…
Detection and construction of an elliptic solution to the complex cubic-quintic Ginzburg-Landau equation
Robert Conte, Tuen-Wai Ng
In evolution equations for a complex amplitude, the phase obeys a much more intricate equation than the amplitude. Nevertheless, general methods should be applicable to both variab…
Exact meromorphic stationary solutions of the real cubic Swift-Hohenberg equation
Robert Conte, Tuen-Wai Ng, Kwok-Kin Wong
We show that all meromorphic solutions of the stationary reduction of the real cubic Swift-Hohenberg equation are elliptic or degenerate elliptic. We then obtain them all explicitl…