26 citations · 42 across the 6 of their papers we have counts for
7 papers
Soliton and breather interactions in the integrable discrete focusing Manakov system via Hirota's method
Uyen Le, Alexander Chernyavsky, Barbara Prinari
The aim of this paper is to apply Hirota's bilinear method to the integrable discrete Manakov system in the focusing dispersion regime in order to construct and analyze soliton and…
Periodic waves of the modified KdV equation as minimizers of a new variational problem
Uyen Le, Dmitry E. Pelinovsky
Periodic waves of the modified Korteweg-de Vries (mKdV) equation are identified in the context of a new variational problem with two constraints. The advantage of this variational…
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…
Convergence of Petviashvili's method near periodic waves in the fractional Korteweg-de Vries equation
Uyen Le, Dmitry E. Pelinovsky
Petviashvili's method has been successfully used for approximating of solitary waves in nonlinear evolution equations. It was discovered empirically that the method may fail for ap…