4 papers
Green's function for the fractional KdV equation on the periodic domain via Mittag-Leffler's function
Uyen Le, Dmitry E. Pelinovsky
The linear operator , where and is the fractional Laplacian on the periodic domain, arises in the existence of periodic travelling waves in the…
Asymptotic stability of viscous shocks in the modular Burgers equation
Uyen Le, Dmitry E. Pelinovsky, Pascal Poullet
Dynamics of viscous shocks is considered in the modular Burgers equation, where the time evolution becomes complicated due to singularities produced by the modular nonlinearity. We…
Periodic waves in the fractional modified Korteweg--de Vries equation
Fábio Natali, Uyen Le, Dmitry E. Pelinovsky
Periodic waves in the modified Korteweg-de Vries (mKdV) equation are revisited in the setting of the fractional Laplacian. Two families of solutions in the local case are given by…
New variational characterization of periodic waves in the fractional Korteweg-de Vries equation
Fabio Natali, Uyen Le, Dmitry E. Pelinovsky
Periodic waves in the fractional Korteweg-de Vries equation have been previously characterized as constrained minimizers of energy subject to fixed momentum and mass. Here we chara…