Existence and orbital stability of standing waves for the 1D Schrödinger-Kirchhoff equation
نویسندگان
چکیده
In this paper we establish the orbital stability of standing wave solutions associated to one-dimensional Schrödinger-Kirchhoff equation. The presence a mixed term gives us more dispersion, and consequently, different scenario for solitary waves in contrast with corresponding nonlinear Schrödinger For periodic waves, exhibit two explicit prove energy space.
منابع مشابه
Existence and Orbital Stability of Cnoidal Waves for a 1D Boussinesq Equation
We will study the existence and stability of periodic travelling-wave solutions of the nonlinear one-dimensional Boussinesq-type equation Φtt −Φxx + aΦxxxx − bΦxxtt +ΦtΦxx + 2ΦxΦxt = 0. Periodic travelling-wave solutions with an arbitrary fundamental period T0 will be built by using Jacobian elliptic functions. Stability (orbital) of these solutions by periodic disturbances with period T0 will ...
متن کاملOrbital Stability for Periodic Standing Waves of the Klein-gordon-zakharov System and the Beam Equation
The existence and stability of spatially periodic waves (eφω, ψω) in the KleinGordon-Zakharov (KGZ) system are studied. We show a local existence result for low regularity initial data. Then, we construct a one-parameter family of periodic dnoidal waves for (KGZ) system when the period is bigger than √ 2π. We show that these waves are stable whenever an appropriate function satisfies the standa...
متن کاملThe Fourth-Order Dispersive Nonlinear Schrödinger Equation: Orbital Stability of a Standing Wave
Considered in this report is the one-dimensional fourth-order dispersive cubic nonlinear Schrödinger equation with mixed dispersion. Orbital stability, in the energy space, of a particular standing-wave solution is proved in the context of Hamiltonian systems. The main result is established by constructing a suitable Lyapunov function.
متن کاملOn Asymptotic Stability of Standing Waves of Discrete Schrödinger Equation in Z
We prove an analogue of a classical asymptotic stability result of standing waves of the Schrödinger equation originating in work by Soffer and Weinstein. Specifically, our result is a transposition on the lattice Z of a result by Mizumachi [M1] and it involves a discrete Schrödinger operator H = −∆+q. The decay rates on the potential are less stringent than in [M1], since we require q ∈ l1,1. ...
متن کاملA ug 2 00 8 ON ASYMPTOTIC STABILITY OF STANDING WAVES OF DISCRETE SCHRÖDINGER EQUATION IN
We prove an analogue of a classical asymptotic stability result of standing waves of the Schrödinger equation originating in work by Soffer and Weinstein. Specifically, our result is a transposition on the lattice Z of a result by Mizumachi [M1] and it involves a discrete Schrödinger operator H = −∆+q. The decay rates on the potential are less stringent than in [M1], since we require q ∈ l1,1. ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2021
ISSN: ['0022-247X', '1096-0813']
DOI: https://doi.org/10.1016/j.jmaa.2021.125098