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High-speed kinks in a generalized discrete phi4 model.

Sergey V Dmitriev1, Avinash Khare, Panayotis G Kevrekidis

  • 1Institute for Metals Superplasticity Problems RAS, 39 Khalturina, Ufa 450001, Russia.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|July 23, 2008
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Summary
This summary is machine-generated.

This study shows that generalized discrete phi4 models can have exact, high-velocity kink solutions. These stable, moving kinks are derived using an integrable mapping, offering insights into nonlinear dynamics.

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Area of Science:

  • Nonlinear dynamics
  • Mathematical physics
  • Condensed matter theory

Background:

  • Discrete phi4 models are crucial for understanding nonlinear phenomena.
  • Exact solutions are vital for validating theoretical models and numerical simulations.
  • Investigating moving kink solutions reveals fundamental properties of solitons.

Purpose of the Study:

  • To explore the existence and properties of exact moving kink solutions in a generalized discrete phi4 model.
  • To determine the conditions under which these solutions are supported and their dependence on velocity.
  • To analyze the integrability and stability of these high-speed kink solutions.

Main Methods:

  • Analytical derivation of kink solutions for the generalized discrete phi4 model.
  • Reduction of a three-point map to a two-point map to demonstrate integrability.
  • Iterative derivation of exact moving solutions based on specific velocities.
  • Perturbation analysis to assess the stability of the obtained solutions.

Main Results:

  • Exact moving kink solutions, shaped as tanh, exist for the generalized discrete phi4 model with arbitrarily large velocities.
  • The existence and form of these solutions are contingent upon specific propagation velocities.
  • The problem of finding these solutions is shown to be integrable for specific velocities, reducible to a two-point map.
  • High-speed kinks exhibit stability and robustness against initial condition perturbations.

Conclusions:

  • Generalized discrete phi4 models can support stable, exact moving kink solutions.
  • The integrability of these models allows for analytical solutions dependent on velocity.
  • These findings contribute to the understanding of solitons and nonlinear wave propagation in discrete systems.