26 citations · 42 across the 29 of their papers we have counts for
33 papers · 1 filter
Existence and spectral stability of small-amplitude periodic waves for the 2D nonlinear focusing Schrodinger equation
Fabio Natali
The purpose of this paper is to establish the existence and spectral stability, with respect to perturbations of the same period, of double-periodic standing waves for the nonlinea…
Periodic Waves for the Regularized Camassa-Holm Equation: Existence and Spectral Stability
Fabio Natali
In this paper, we investigate the existence and spectral stability of periodic traveling wave solutions for the regularized Camassa-Holm equation. To establish the existence of per…
On the orbital stability of solitary waves for the fourth order nonlinear Schrödinger equation
Handan Borluk, Gulcin M. Muslu, Fábio Natali
In this paper, we present new results regarding the orbital stability of solitary standing waves for the general fourth-order Schrödinger equation with mixed dispersion. The existe…
Stability of Periodic Waves for the Defocusing Fractional Cubic Nonlinear Schrödinger Equation
Handan Borluk, Gulcin M. Muslu, Fábio Natali
In this paper, we determine the spectral instability of periodic odd waves for the defocusing fractional cubic nonlinear Schrödinger equation. Our approach is based on periodic per…
Transverse instability of periodic standing waves for the generalized nonlinear Schrodinger equation
Fabio Natali, Gabriel E. Bittencourt Moraes
In this paper, we determine the transverse instability of periodic standing wave solutions for the generalized Schrödinger equation with fractional power nonlinearity. The existenc…
Spectral Stability of Periodic Traveling Wave Solutions for a Double Dispersion Equation
Fábio Natali, Thiago P. de Andrade
In this paper, we investigate the spectral stability of periodic traveling waves for a cubic-quintic and double dispersion equation. Using the quadrature method we find explict per…
Transversal spectral instability of periodic traveling waves for the generalized Zakharov-Kuznetsov equation
Fabio Natali
In this paper, we determine the transversal instability of periodic traveling wave solutions of the generalized Zakharov-Kuznetsov equation in two space dimensions. Using an adapta…
Spectral stability of multiple periodic waves for the Schrodinger system with cubic nonlinearity
Fábio Natali, Gabriel E. Bittencourt Moraes
Results concerning the existence and spectral stability and instability of multiple periodic wave solutions for the nonlinear Schrödinger system with \textit{dnoidal} and \textit{c…
Orbital Stability of Periodic Traveling Waves for the "abcd" Boussinesq Systems
Gabriel E. Bittencourt Moraes, Guilherme de Loreno, Fábio Natali
New results concerning the orbital stability of periodic traveling wave solutions for the "abcd" Boussinesq model will be shown in this manuscript. For the existence of solutions,…
Orbital stability of periodic standing waves for the cubic fractional nonlinear Schrodinger equation
Gabriel E. Bittencourt Moraes, Handan Borluk, Guilherme de Loreno +2
In this paper, the existence and orbital stability of the periodic standing waves solutions for the nonlinear fractional Schrodinger (fNLS) equation with cubic nonlinearity is stud…
Periodic waves for the cubic-quintic non-linear Schrödinger equation: existence and orbital stability
Giovana Alves, Fabio Natali
In this paper, we prove existence and orbital stability results of periodic standing waves for the cubic-quintic nonlinear Schrödinger equation. We use the implicit function theore…
On the Stability of Solitary Wave Solutions for a Generalized Fractional Benjamin-Bona-Mahony Equation
Goksu Oruc, Fábio Natali, Handan Borluk +1
In this paper we establish a rigorous spectral stability analysis for solitary waves associated to a generalized fractional Benjamin-Bona-Mahony type equation. Besides the well kno…
Cnoidal Waves for the cubic nonlinear Klein-Gordon and Schrödinger Equations
Guilherme de Loreno, Gabriel E. B. Moraes, Fábio Natali +1
In this paper, we establish orbital stability results for \textit{cnoidal} periodic waves of the cubic nonlinear Klein-Gordon and Schrödinger equations in the energy space restrict…
On the existence, uniqueness and stability of Periodic Waves for the fractional Benjamin-Bona-Mahony equation
Sabrina Amaral, Handan Borluk, Gulcin M. Muslu +2
The existence, uniqueness and stability of periodic traveling waves for the fractional Benjamin-Bona-Mahony equation is considered. In our approach, we give sufficient conditions t…
Stability of smooth periodic traveling waves in the Camassa-Holm equation
Anna Geyer, Renan H. Martins, Fábio Natali +1
Smooth periodic travelling waves in the Camassa--Holm (CH) equation are revisited. We show that these periodic waves can be characterized in two different ways by using two differe…
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…
Odd Periodic Waves for some Klein-Gordon Type Equations: Existence and Stability
Fábio Natali, Guilherme de Loreno
In this paper, we establish the existence and stability properties of odd periodic waves related to the Klein-Gordon type equations, which include the well known and mo…
Existence and orbital stability of standing waves for the 1D Schrödinger-Kirchhoff equation
Fábio Natali, Eleomar Cardoso
In this paper we establish the orbital stability of standing wave solutions associated to the one-dimensional Schrödinger-Kirchhoff equation. The presence of a mixed term gives us…
On the spectral stability of periodic traveling waves for the critical Korteweg-de Vries and Gardner equations
Fábio Natali, Sabrina Amaral, Eleomar Cardoso
In this paper, we determine spectral stability results of periodic waves for the critical Korteweg-de Vries and Gardner equations. For the first equation, we show that both positiv…
A comment about the paper On the instability of elliptic traveling wave solutions of the modified Camassa-Holm equation
Fábio Natali, Renan H. Martins
We discuss the recent paper by A. Darós and L.K. Arruda (On the instability of elliptic traveling wave solutions of the modified Camassa-Holm equation, J. Diff. Equat., 266 (2019),…
Orbital Stability of Periodic Standing Waves for the Logarithmic Klein-Gordon Equation
Fábio Natali, Eleomar Cardoso
The main goal of this paper is to present orbital stability results of periodic standing waves for the one-dimensional logarithmic Klein-Gordon equation. To do so, we first use com…
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…
On the Stability of Periodic Traveling Waves for the Modified Kawahara Equation
Gisele Detomazi Almeida, Fabrício Cristófani, Fábio Natali
In this paper, we present the first result concerning the orbital stability of periodic traveling waves for the modified Kawahara equation. Our method is based on the Fourier expan…
Instability of -stable peakons in the Camassa-Holm equation
Fabio Natali, Dmitry E. Pelinovsky
It is well-known that peakons in the Camassa-Holm equation are -orbitally stable thanks to the presence of conserved quantities and properties of peakons as constrained energy…