Search

We prove the orbital stability of soliton solutions for 2D Maxwell–Lorentz system with extended charged particle. The solitons corresponds to the uniform motion and rotation of the particle.We reduce the corresponding Hamilton system by the canonical transformation via transition to a comoving frame. The solitons are the critical points of the reduced Hamiltonian. The key point of the proof is a lower bound for the Hamiltonian. [ABSTRACT FROM AUTHOR] more...

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 [2,14] which give us sufficient conditions to the orbital stability for a general class of evolution equations. [ABSTRACT FROM AUTHOR] more...

We study the existence and orbital stability of standing waves of nonlinear fractional Schrödinger equations with a general nonlinear term. The existence and non-existence of global minimizers with respect to Eα are established for all possible values of α: Under some general assumptions on the nonlinear term f(u), there exists a constant α0 > 0 such that a global minimizer exists for Eα for all α > α0, and there is no global minimizer with respect to Eα for all 0 < α < α0: By virtue of concentration-compactness argument and the strict subadditivity of Eα, the strong convergence of minimizing sequence is obtained. Moreover, we present some criteria which determine α0 = 0 or α0 > 0, and the existence of global minimizers for Eα0: Besides, we show the orbital stability of the global minimizers set. Finally, we prove that an energy minimizer is a least action solution by Pohozaev identity. [ABSTRACT FROM AUTHOR] more...

We obtain explicit characterization of orbital and spectral stability of solitary wave solutions to the U(1)-invariant 1D Klein–Gordon equation coupled to an anharmonic oscillator. We also give the complete analysis of the spectrum of the linearization at a solitary wave. [ABSTRACT FROM AUTHOR] more...

We prove the orbital stability of periodic traveling-wave solutions for systems of dispersive equations with coupled nonlinear terms. Our method is basically developed under two assumptions: one concerning the spectrum of the linearized operator around the traveling wave and another one concerning the existence of a conserved quantity with suitable properties. The method can be applied to several systems such as the Liu-Kubota-Ko system, the modified KdV system and a log-KdV type system. [ABSTRACT FROM AUTHOR] more...

In this paper we study the existence and orbital stability of ground states for logarithmic Schrödinger equation under a constant magnetic field. For this purpose we establish the well-posedness of the Cauchy Problem in a magnetic Sobolev space and an appropriate Orlicz space. Then we show the existence of ground state solutions via a constrained minimization on the Nehari manifold. We also show that the ground state is orbitally stable. [ABSTRACT FROM AUTHOR] more...