5 papers
Discrete quantum harmonic oscillator and Kravchuk transform
Quentin Chauleur, Erwan Faou
We consider a particular discretization of the harmonic oscillator which admits an orthogonal basis of eigenfunctions called Kravchuk functions possessing appealing properties from…
Around plane waves solutions of the Schr{ö}dinger-Langevin equation
Quentin Chauleur, Erwan Faou
We consider the logarithmic Schr{ö}dinger equations with damping, also called Schr{ö}dinger-Langevin equation. On a periodic domain, this equation possesses plane wave solutions th…
The isothermal limit for the compressible Euler equations with damping
Quentin Chauleur
We consider the isothermal Euler system with damping. We rigorously show the convergence of Barenblatt solutions towards a limit Gaussian profile in the isothermal limit $\righ…
Global dissipative solutions of the defocusing isothermal Euler-Langevin-Korteweg equation
Quentin Chauleur
We construct global dissipative solutions on the torus of dimension at most three of the defocusing isothermal Euler-Langevin-Korteweg system, which corresponds to the Euler-Kortew…
Dynamics of the Schr{ö}dinger-Langevin Equation
Quentin Chauleur
We consider the nonlinear Schr{ö}dinger-Langevin equation for both signs of the logarithmic nonlinearity. We explicitly compute the dynamics of Gaussian solutions for large times,…