Preprints
F. Natali, Periodic waves for the regularized Camassa-Holm equation: existence and spectral stability (2024), in preparation.
F. Natali, H. Borluk and G. Muslu, On the orbital stability of solitary waves for the fourth order nonlinear Schrödinger equation (2024).
F. Natali, Remarks on the orbital stability for the sine-Gordon equation (2024).
F. Natali and G.E. Bittencourt Moraes, Transverse instability of periodic standing waves for the generalized nonlinear Schrodinger equation (2023).
F. Natali, Transversal spectral instability of periodic traveling waves for the generalized Zakharov-Kuznetsov equation (2023), accepted.
F. Natali, G.E. Bittencourt Moraes, G. de Loreno and A. Pastor, Cnoidal waves for the cubic nonlinear Klein-Gordon and Schrodinger equations (2023).
F. Natali and G.E. Bittencourt Moraes, Spectral stability of multiple periodic waves for the Schrödinger system with cubic nonlinearity (2023), accepted.
Book chapter
F. Natali and J. Angulo, Orbital stability of periodic traveling wave solutions. Fourier Transforms-Approach to Scientific Principles, Theory-Methodology-Applications - Intech (2011).
Published papers
F. Natali and T.P. de Andrade, Spectral stability of periodic traveling wave solutions for a cubic-quintic and double dispersion equation, Applicable Analysis (2024).
F. Natali and G. Alves, Monotonicity of the period map for the equation -\varphi''+\varphi-\varphi^{k}=0, Monatshefte für Mathematik (2024).
F. Natali, H. Borluk and G. Muslu, Stability of periodic waves for the defocusing fractional cubic nonlinear Schrodinger equation, Communications in Nonlinear Sciences and Numerical Simulation (2024).
F. Natali and G. de Loreno, Odd periodic waves for some Klein-Gordon type equations: existence and stability, Mathematical Methods in the Applied Sciences, (2023).
F. Natali, G.E. Bittencourt Moraes and G. de Loreno, Orbital stability of periodic traveling waves for the "abcd" Boussinesq systems, Communications on Pure and Applied Analysis (2023).
F. Natali, H. Borluk, G. de Loreno, G.E. Bittencourt Moraes, G. Muslu, Orbital stability of periodic standing waves for the cubic fractional nonlinear Schrödinger equation, Journal of Differential Equations (2022).
F. Natali, G. Oruc, H. Borluk and G. Muslu, On the stability of solitary wave solutions for a generalized fractional Benjamin-Bona-Mahony equation, Nonlinearity (2022).
F. Natali and G. Alves, Periodic waves for the cubic-quintic nonlinear Schrodinger equation: existence and orbital stability, Discrete and Continuous Dynamical Systems - Series B (2022).
F. Natali, S. Amaral, H. Borluk, G. Muslu and G. Oruc, On the existence, uniqueness and stability of periodic waves for the fractional Benjamin-Bona-Mahony equation, Studies in Applied Mathematics (2022).
F. Natali, A. Geyer, R. Martins and D. Pelinovsky, Stability of smooth periodic traveling waves in the Camassa-Holm equation, Studies in Applied Mathematics (2022).
F. Natali, U. Le and D. Pelinovsky, Correction to: Periodic Waves in the Fractional Modified Korteweg-de Vries Equation. Journal of Dynamics and Differential Equations (2022).
F. Natali, U. Le and D. Pelinovsky, Periodic waves in the fractional modified Korteweg-de Vries equation. Journal of Dynamics and Differential Equations (2022).
F. Natali and S. Amaral. On the instability of periodic waves for dispersive equations - Revisited. Nagoya Mathematical Journal (2022).
F. Natali and E. Cardoso Jr. Existence and orbital stability of standing waves for the 1D Schrödinger-Kirchhoff equation. Journal of Mathematical Analysis and Applications (2021).
F. Natali, S. Amaral and E. Cardoso Jr. On the spectral stability of periodic traveling waves for the critical Korteweg-de Vries and Gardner equations. SN Partial Differential Equations and Applications (2021).
F. Natali and D. Pelinovsky, Instability of H1-stable peakons in the Camassa-Holm equation. Journal of Differential Equations (2020).
F. Natali and E. Cardoso Jr., Orbital stability of periodic standing waves for the logarithmic Klein-Gordon equation. Journal of Mathematical Analysis and Applications (2020).
F. Natali, U. Le and D. Pelinovsky, New variational characterization of periodic waves in the fractional Korteweg-de Vries equation. Nonlinearity (2020).
F. Natali, F. Cristófani and A. Pastor, Periodic Traveling-wave solutions for regularized dispersive equations: Sufficient conditions for orbital stability with applications. Communications in Mathematical Sciences (2020).
F. Natali and R. Martins, A comment about the paper -On the instability of elliptic traveling wave solutions of the modified Camassa-Holm equation-. Journal of Differential Equations (2020).
F. Natali, G. Alves and A. Pastor, Sufficient conditions for orbital stability of periodic traveling waves. Journal of Differential Equations (2019).
F. Natali, F. Cristófani and G.D. Almeida, On the stability of periodic traveling waves for the modified Kawahara equation. Applicable Analysis (2019).
F. Natali, Orbital stability of periodic traveling-wave solutions for a dispersive equation. São Paulo Journal of Mathematical Sciences (2019).
F. Natali and S. Amaral, Odd periodic waves and stability results for the defocusing mass-critical Korteweg-de Vries equation. Mathematical Methods in the Applied Sciences (2019).
F. Natali, E. Cardoso Jr. and A. Pastor, Well-Posedness and orbital stability of periodic traveling waves for Schamel's equation. Zeitschrift fur Analysis und ihre Anwendung (2018).
F. Natali, E. Cardoso Jr. and J. Angulo, Stability properties of periodic traveling waves for the intermediate long wave equation. Revista Matematica Iberoamericana (2017).
F. Natali, T.P. Andrade and F. Cristófani, Orbital stability of periodic traveling wave solutions for the Kawahara equation. Journal of Mathematical Physics. (2017).
F. Natali, F. Cristófani and A. Pastor, Orbital stability of periodic traveling-wave solutions for the log-KdV equation. Journal of Differential Equations (2017).
F. Natali, A note on the exponential decay for the nonlinear Schrodinger equation. Osaka Journal of Mathematics (2016).
F. Natali and G.G. Doronin, Exponential decay for a locally damped fifth-order equation posed on the line. Nonlinear Analysis Real World Applications (2016).
F. Natali and J. Angulo, On the instability of periodic waves for dispersive equations. Differential and Integral Equations (2016).
F. Natali and A. Pastor, The fourth-order dispersive nonlinear Schrödinger equation: orbital stability of a standing wave. SIAM Journal on Applied Dynamical Systems (2015).
F. Natali, Exponential stabilization for the nonlinear Schrödinger equation with localized damping. Journal of Dynamical and Control Systems (2015).
F. Natali and A. Pastor, Orbital instability of standing waves for the quadratic-cubic Klein-Gordon-Schrödinger system. Zeitschrift fur Angewandte Mathematik und Physik (2014).
F. Natali and G.G. Doronin, An example of non-decreasing solution for the KdV equation posed on a bounded interval. Comptes Rendu Mathématique (2014).
F. Natali and J. Angulo, (Non)linear instability of periodic traveling waves: Klein-Gordon and KdV type equations. Advances in Nonlinear Analysis (2014).
F. Natali and A. Neves, Orbital stability of periodic waves. IMA Journal of Applied Mathematics (2013).
F. Natali and E. Cardoso Jr. Stability properties of periodic waves for the Klein-Gordon equation with quintic nonlinearity. Applied Mathematics and Computation (2013).
F. Natali, M.M. Cavalcanti, V.N.D. Cavalcanti and A. Faminskii, Decay of solutions to damped Korteweg-de Vries type equation. Applied Mathematics and Optimization (2012).
F. Natali and A. Pastor, Orbital stability of periodic waves for the Klein-Gordon-Schrodinger system. Discrete and Continuous Dynamical Systems - Series A (2011).
F. Natali, On periodic waves for sine and sinh-Gordon equations. Journal of Mathematical Analysis and Applications (2011).
F. Natali and A. Pastor, Stability properties of periodic standing waves for the Klein-Gordon-Schrödinger system. Communications on Pure Applied Analysis (2010).
F. Natali, A note on the stability for Kawahara-KdV type equations. Applied Mathematics Letters (2010).
F. Natali, M.M. Cavalcanti, V.N.D. Cavalcanti, J. Soriano, Qualitative aspects for the cubic nonlinear Schrödinger equations with localized damping: exponential and polynomial stabilization. Journal of Differential Equations (2010).
F. Natali, Unstable snoidal waves. Journal of the London Mathematical Society (2010).
F. Natali and J. Angulo, Stability and instability of periodic travelling wave solutions for the critical Korteweg-de Vries and nonlinear Schrödinger equations. Physica D (2009).
F. Natali, M.M. Cavalcanti, V.N.D. Cavalcanti and R. Fukuoka, Exponential stability for the 2D defocusing Schrodinger equation with locally distributed damping. Differential and Integral Equations (2009).
F. Natali and A. Pastor, Stability and instability of periodic standing wave solutions for some Klein-Gordon equations, Journal of Mathematical Analysis and Applications (2008).
F. Natali and J. Angulo, Positivity Properties of the Fourier Transform and the Stability of Periodic Travelling-Wave Solutions, SIAM Journal on Mathematical Analysis (2008).