kinks - gradient flow and dynamics

  title={kinks - gradient flow and dynamics},
  author={N. S. Manton and Houari Merabet},
The symmetric dynamics of two kinks and one antikink in classical (1 + 1)-dimensional theory is investigated. Gradient flow is used to construct a collective coordinate model of the system. The relationship between the discrete vibrational mode of a single kink, and the process of kink - antikink pair production is explored. 
Resonance structures in coupled two-componentϕ4model
We present a numerical study of the process of the kink-antikink collisions in the coupled one-dimensional two-component $\phi^4$ model. Our results reveal two different soliton solutions which
Quasinormal modes in kink excitations and kink–antikink interactions: a toy model
We study excitations and collisions of kinks in a scalar field theory where the potential has two minima with $$Z_2$$Z2 symmetry. The field potential is designed to create a square well potential in
Iterated ϕ4 kinks
Abstract A first order equation for a static ϕ 4 kink in the presence of an impurity is extended into an iterative scheme. At the first iteration, the solution is the standard kink, but at the
Wobbling kinks in varphi(4) theory.
The complex amplitude of the wobbling mode is shown to obey a simple ordinary differential equation with nonlinear damping and the t(-1/2)-decay law is confirmed, which was previously obtained on the basis of energy considerations.
Fermions on kinks revisited
We study fermion modes localized on the kink in the 1+1 dimensional $\phi^4$ model, coupled to the Dirac fermions with backreaction. Using numerical methods we construct self-consistent solutions of
False vacuum decay in kink scattering
A bstractIn this work we consider kink-antikink and antikink-kink collisions in a modified ϕ4 model with a false vacuum characterized by a dimensionless parameter ϵ. The usual ϕ4 model is recovered
Dynamics of lattice kinks
Abstract We consider a class of Hamiltonian nonlinear wave equations governing a field defined on a spatially discrete one-dimensional lattice, with discreteness parameter, d = h −1 , where h >0 is
Boundary scattering in the phi^4 model
We study boundary scattering in the phi^4 model on a half-line with a one-parameter family of Neumann-type boundary conditions. A rich variety of phenomena is observed, which extends
Some Recent Developments on Kink Collisions and Related Topics
We review recent works on modeling of dynamics of kinks in 1\(+\)1 dimensional \(\phi ^4\) theory and other related models, like sine-Gordon model or \(\phi ^6\) theory. We discuss how the spectral
Oscillons in the presence of external potential
A bstractWe discuss similarity between oscillons and oscillational mode in perturbed ϕ4. For small depths of the perturbing potential it is difficult to distinguish between oscillons and the mode in


Unstable manifolds and soliton dynamics.
  • Manton
  • Physics, Medicine
    Physical review letters
  • 1988
It is argued that the interactions between solitons are well approximated by a finite-dimensional dynamical system, provided that the static forces between the solitons are relatively weak. The
Resonance structure in kink-antikink interactions in φ4 theory
Abstract We present new numerical and theoretical results concerning kink-antikink collisions in the classical (nonintegrable) φ 4 field model in one-dimensional space. Earlier numerical studies of
Collective-coordinate method for quasizero modes
Abstract The collective-coordinate method for the quasizero modes is suggested. Quasizero mode means that a direction in functional space exists where the action varies slowly. As in the case of
Interaction of Superconducting Vortices and Asymptotics of the Ginzburg-Landau Flow
We discuss the interaction of superconducting vortices in the gradient flow of the superconducting Ginzburg-Landau functional. Some conjectures are given and a result on the large time asymptotics of
Wobbling kinks in φ4 and sine‐Gordon theory
When the φ4 model admits a kink solution, it also admits a wobbling kink, which satisfies the boundary conditions of a kink, but possesses an internal degree of freedom. In this paper we develop a
A remark on the scattering of BPS monopoles
Abstract It is shown that the classical dynamics of several slowly moving monopoles corresponds to a geodesic motion in the manifold of exact, static multi-monopole configurations.
Interaction energy of superconducting vortices
By means of a constrained variational calculation we determine the interaction energy of two-vortex configurations in the Ginzburg-Landau theory or, equivalently, in the Abelian Higgs model. The
An effective Lagrangian for solitons
Abstract An effective Lagrangian is proposed for deriving the properties of solitons. The Lagrangian has only local interactions, and involves a new local field to represent the soliton. The soliton
Stability of the B=2 hedgehog in the Skyrme model
Abstract In an attempt to extract the collective Hamiltonian of the baryon-number-two sector of the Skyrme model from exact classical field configurations, we study the unstable modes of the B = 2
Dynamics of Abelian Higgs vortices in the near Bogomolny regime
The aim of this paper is to give an analytical discussion of the dynamics of the Abelian Higgs multi-vortices whose existence was proved by Taubes ([JT82]). For a particular value of a parameter of