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Gabriel E. Bittencourt Moraes

Publications and source records attributed to Gabriel E. Bittencourt Moraes.

6 recordsLinked to original sources
arXiv2026

Schrödinger system with quintic nonlinearity: spectral stability of multiple sign-changing periodic waves

This manuscript investigates the existence and spectral stability of multiple periodic standing wave solutions for a nonlinear Schrödinger system. By considering both cnoidal and snoidal profiles, we provide a comprehensive spectral analysis of the associated linearized operators, employing the Floquet theory and comparison theorems. Stability results are derived under periodic perturbations with the same period as the underlying standing waves. Furthermore, we apply the spectral stability theory via Krein signature to determine the spectral stability and instability results.

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arXiv2024

Spectral stability of multiple periodic waves for the Schrodinger system with cubic nonlinearity

Results concerning the existence and spectral stability and instability of multiple periodic wave solutions for the nonlinear Schrödinger system with \textit{dnoidal} and \textit{cnoidal} profile will be determined in this manuscript. The spectral analysis for the corresponding linearized operator is established by using the comparison theorem and tools of Floquet theory. The main results are determined by applying the spectral stability theory in \cite{KapitulaKevrekidisSandstedeI} and \cite{KapitulaKevrekidisSandstedeII} via Krein signature.

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arXiv2023

Transverse instability of periodic standing waves for the generalized nonlinear Schrodinger equation

In this paper, we determine the transverse instability of periodic standing wave solutions for the generalized Schrödinger equation with fractional power nonlinearity. The existence of periodic waves is determined by using a constrained minimization problem in the complex setting, and it is shown that the corresponding real solution, depending on the power nonlinearity, is always positive or changes its sign. The transverse instability results are then determined by applying the main result given in \cite{RoussetTzvetkov} for the periodic case.

math.AP↗
arXiv2022

Orbital Stability of Periodic Traveling Waves for the "abcd" Boussinesq Systems

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, we use basic tools of ordinary differential equations to show that the corresponding periodic wave depends on the Jacobi elliptic function of cnoidal type. The spectral analysis for the associated linearized operator is determined by using some tools concerning the Floquet theory. The orbital stability is then established by applying the abstract results [2] and [14] which give us sufficient conditions to the orbital stability for a general class of evolution equations.

math.AP↗
arXiv2022

Orbital stability of periodic standing waves for the cubic fractional nonlinear Schrodinger equation

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 studied. The existence is determined by using a minimizing constrained problem in the complex setting and we it is showed that the corresponding real solution is always positive. The orbital stability is proved by combining some tools regarding positive operators, the oscillation theorem for fractional Hill operators and a Vakhitov-Kolokolov condition, well known for Schrodinger equations. We then perform a numerical approach to generate periodic standing wave solutions of the fNLS equation by using the Petviashvili's iteration method. We also investigate the Vakhitov-Kolokolov condition numerically which cannot be obtained analytically for some values of the order of the fractional derivative.

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