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Nonlinear Subharmonic Dynamics of Spectrally Stable Lugiato-Lefever Periodic Waves
Mariana Haragus, Mathew A. Johnson, Wesley R. Perkins +1
We study the nonlinear dynamics of perturbed, spectrally stable -periodic stationary solutions of the Lugiato-Lefever equation (LLE), a damped nonlinear Schrödinger equation wit…
Transverse dynamics of two-dimensional traveling periodic gravity-capillary water waves
Mariana Haragus, Tien Truong, Erik Wahlén
We study the transverse dynamics of two-dimensional traveling periodic waves for the gravity--capillary water-wave problem. The governing equations are the Euler equations for the…
Linear instability of breathers for the focusing nonlinear Schr{ö}dinger equation
Mariana Haragus, Dmitry Pelinovsky
Relying upon tools from the theory of integrable systems, we discuss the linear instability of the Kuznetsov-Ma breathers and the Akhmediev breathers of the focusing nonlinear Schr…
Heteroclinic orbits for a system of amplitude equations for orthogonal domain walls
Boris Buffoni, Mariana Haragus, Gérard Iooss
Using a variational method, we prove the existence of heteroclinic solutions for a 6dimensional system of ordinary differential equations. We derive this system from the classical…
Linear Modulational and Subharmonic Dynamics of Spectrally Stable Lugiato-Lefever Periodic Waves
Mariana Haragus, Mathew A. Johnson, Wesley R. Perkins
We study the linear dynamics of spectrally stable -periodic stationary solutions of the Lugiato-Lefever equation (LLE), a damped nonlinear Schrödinger equation with forcing that…
Transverse instability of periodic and generalized solitary waves for a fifth-order KP model
Mariana Haragus, Erik Wahlén
We consider a fifth-order Kadomtsev-Petviashvili equation which arises as a two-dimensional model in the classical water-wave problem. This equation possesses a family of generaliz…
Numerical study of the stability of the Peregrine breather
C. Klein, M. Haragus
The Peregrine breather is widely discussed as a model for rogue waves in deep water. We present here a detailed numerical study of perturbations of the Peregrine breather as a solu…
Transverse spectral stability of small periodic traveling waves for the KP equation
Mariana Haragus
The Kadomtsev-Petviashvili (KP) equation possesses a four-parameter family of one-dimensional periodic traveling waves. We study the spectral stability of the waves with small ampl…
Orbital stability of periodic waves for the nonlinear Schroedinger equation
Thierry Gallay, Mariana Haragus
The nonlinear Schroedinger equation has several families of quasi-periodic travelling waves, each of which can be parametrized up to symmetries by two real numbers: the period of t…
Stability of small periodic waves for the nonlinear Schroedinger equation
Thierry Gallay, Mariana Haragus
The nonlinear Schroedinger equation possesses three distinct six-parameter families of complex-valued quasi-periodic travelling waves, one in the defocusing case and two in the foc…