相关论文: On the orbital stability of standing-waves solutio…

In this work we prove the existence of standing-wave solutions to the scalar non-linear Klein-Gordon equation in dimension one and the stability of the ground-state, the set which contains all the minima of the energy constrained to the…

In this paper, we study the standing wave solutions of Klein--Gordon equation with logarithmic nonlinearity. The existence of the standing wave solution related to the ground state $\phi_0(x)$ is obtained. Further, we prove the instability…

We consider a system of nonlinear Klein-Gordon equations with quadratic interaction in two and three space dimensions. The strong instability of standing wave solutions is studied for the system without assuming the mass resonance…

We study the stability of standing-waves solutions to a scalar non-linear Klein-Gordon equation in dimension one with a quadratic-cubic non-linearity. Orbits are obtained by applying the semigroup generated by the negative complex unit…

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 compactness arguments and a non-standard analysis to obtain the…

In this paper, we consider radial standing waves to a nonlinear Klein-Gordon equation with a repulsive inverse-square potential. It is known that existence of a "radial" ground state to the stationary problem of the nonlinear Klein-Gordon…

This paper is concerned with strong blow-up instability (Definition 1.3) for standing wave solutions to the system of the quadratic nonlinear Klein-Gordon equations. In the single case, namely the nonlinear Klein-Gordon equation with power…

We investigate the orbital stability and instability of standing waves for two classes of Klein-Gordon equations in the semi-classical regime.

In this paper, we study local well-posedness and orbital stability of standing waves for a singularly perturbed one-dimensional nonlinear Klein-Gordon equation. We first establish local well-posedness of the Cauchy problem by a fixed point…

In this paper we study existence and orbital stability for solitary waves of the nonlinear Klein-Gordon equation. The energy of these solutions travels as a localized packet, hence they are a particular type of solitons. In particular we…

We show the existence of ground state and orbital stability of standing waves of fractional Schr\"{o}dinger equations with power type nonlinearity. For this purpose we establish the uniqueness of weak solutions.

We study the existence and orbital stability/instability of periodic standing wave solutions for the Klein-Gordon-Schr\"odinger system with Yukawa and cubic interactions. We prove the existence of periodic waves depending on the Jacobian…

We prove the existence of normalized ground state solutions for the biharmonic Schr\"odinger equation with combined nonlinearities and show that all ground states correspond to the local minima of the associated energy functional restricted…

In this paper we prove the existence of a ground state solution for the nonlinear Klein-Gordon-Maxwell equations in the electrostatic case.

We investigate the stability and long-term behavior of spatially periodic plane waves in the complex Klein-Gordon equation under localized perturbations. Such perturbations render the wave neither localized nor periodic, placing its…

Considered in this report is the one-dimensional fourth-order dispersive cubic nonlinear Schr\"odinger equation with mixed dispersion. Orbital stability, in the energy space, of a particular standing-wave solution is proved in the context…

We study local well-posedness and orbital stability/instability of standing waves for a first order system associated with a nonlinear Klein-Gordon equation on a star graph. The proof of the well-posedness uses a classical fixed point…

In this paper we establish the orbital stability of standing wave solutions associated to the one-dimensional Schr\"odinger-Kirchhoff equation. The presence of a mixed term gives us more dispersion, and consequently, a different scenario…

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…

We introduce mountain-pass type arguments in the context of orbital instability for Klein-Gordon equations. Our aim is to illustrate on two examples how these arguments can be useful to simplify proofs and derive new results of orbital…