On Asymptotic Stability in 3d of Kinks for the Φ Model
نویسندگان
چکیده
We add to a kink, which is a 1 dimensional structure, two transversal directions. We then check its asymptotic stability with respect to compactly supported perturbations in 3D and a time evolution under a Nonlinear Wave Equation (NLW). The problem is inspired by work by Jack Xin on asymptotic stability in dimension larger than 1 of fronts for reaction diffusion equations. The proof involves a separation of variables. The transversal variables are treated as in work on Nonlinear Klein Gordon Equation (NLKG) originating from Klainerman and from Shatah in a particular elaboration due to Delort et al. The longitudinal variable is treated by means of a result by Weder on dispersion for Schrödinger operators in 1D. §
منابع مشابه
Permanence and Uniformly Asymptotic Stability of Almost Periodic Positive Solutions for a Dynamic Commensalism Model on Time Scales
In this paper, we study dynamic commensalism model with nonmonotic functional response, density dependent birth rates on time scales and derive sufficient conditions for the permanence. We also establish the existence and uniform asymptotic stability of unique almost periodic positive solution of the model by using Lyapunov functional method.
متن کاملTravelling kinks in discrete φ 4 models
In recent years, three exceptional discretizations of the φ 4 model have been discovered [S97, BT97, K03] which support translationally invariant kinks, i.e., families of stationary kinks centered at arbitrary points between the lattice sites. We address the question of the persistence of these kinks for nonzero velocity. By computing the Stokes constants in beyond-all-order asymptotic expansio...
متن کاملPermanence and global asymptotic stability of a delayed predator-prey model with Hassell-Varley type functional response
Here, a predator-prey model with Hassell-Varley type functional responses is studied. Some sufficient conditions are obtained for the permanence and global asymptotic stability of the system by using comparison theorem and constructing a suitable Lyapunov functional. Moreover, an example is illustrated to verify the results by simulation.
متن کاملct 2 00 5 Travelling kinks in discrete φ 4 models
In recent years, three exceptional discretizations of the φ 4 theory have been discovered [SW94, BT97, K03] which support translationally invariant kinks, i.e. families of stationary kinks centred at arbitrary points between the lattice sites. It has been suggested that the translationally invariant stationary kinks may persist as sliding kinks, i.e. discrete kinks travelling at nonzero velocit...
متن کاملدینامیک سالیتونهای مدل 6 φ در یک پتانسیل خارجی
In this paper, we study particle aspects of the φ6 kinks in an external potential. The external potential is implemented by breaking the translational invariance of the system. The dynamics of the kink is calculated for the simple harmonic oscillator (SHO) and barrier potentials. The periodic motion of the kink in the SHO case is compared to the corresponding ordinary (classical) motion. It i...
متن کامل