127 citations · 780 across the 73 of their papers we have counts for
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All meromorphic traveling waves of cubic and quintic complex Ginzburg-Landau equations
Robert Conte, Micheline Musette, Ng Tuen Wai +1
For both cubic and quintic nonlinearities of the one-dimensional complex Ginzburg-Landau evolution equation, we prove by a theorem of Eremenko the finiteness of the number of trave…
New solutions to the complex Ginzburg-Landau equations
Robert Conte, Micheline Musette, Ng Tuen Wai +1
The various régimes observed in the one-dimensional complex Ginzburg-Landau equation result from the interaction of a very small number of elementary patterns such as pulses, front…
Explicit breather solution of the nonlinear Schrödinger equation
Robert Conte, ENS Paris-Saclay
We present a one-line closed form expression for the three-parameter breather of the nonlinear Schrödinger equation. This provides an analytic proof of the time period doubling obs…
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…
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 internal waves of a Boussinesq system
Hai Yen Nguyen, Fre'de'ric Dias, Robert Conte
We consider a Boussinesq system describing one-dimensional internal waves which develop at the boundary between two immiscible fluids, and we restrict to its traveling waves. The m…
Ginzburg-Landau equation for dynamical four-wave mixing in gain nonlinear media with relaxation
Svitlana Bugaychuk, Robert Conte
We consider the dynamical degenerate four-wave mixing (FWM) model in a cubic nonlinear medium including both the time relaxation of the induced nonlinearity and the nonlocal coupli…
Doubly periodic waves of a discrete nonlinear Schrödinger system with saturable nonlinearity
Robert Conte, Kwok-wing Chow
A system of two discrete nonlinear Schrödinger equations of the Ablowitz-Ladik type with a saturable nonlinearity is shown to admit a doubly periodic wave, whose long wave limit is…
Analytic structure of the four-wave mixing model in photorefractive materials
Robert Conte, Svetlana Bugaychuk
In order to later find explicit analytic solutions, we investigate the singularity structure of a fundamental model of nonlinear optics, the four-wave mixing model in one space var…
Periodic waves of a discrete higher order nonlinear Schroedinger equation
Robert Conte, Kwok-wing Chow
The Hirota equation is a higher order extension of the nonlinear Schroedinger equation by incorporating third order dispersion and one form of self steepening effect. New periodic…
Analytic doubly periodic wave patterns for the integrable discrete nonlinear Schroedinger (Ablowitz-Ladik) model
K. W. Chow, Robert Conte, Neil Xu
We derive two new solutions in terms of elliptic functions, one for the dark and one for the bright soliton regime, for the semi-discrete cubic nonlinear Schroedinger equation of A…
Solitary waves of nonlinear nonintegrable equations
Robert Conte, Micheline Musette
Our goal is to find closed form analytic expressions for the solitary waves of nonlinear nonintegrable partial differential equations. The suitable methods, which can only be nonpe…
Analytic solitary waves of nonintegrable equations
M. Musette, R. Conte
Even if it is nonintegrable, a differential equation may nevertheless admit particular solutions which are globally analytic. On the example of the dynamical system of Kuramoto and…