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Nonlinear modulation of multidimensional lattice waves.

G Huang1, V V Konotop, H W Tam

  • 1Key Laboratory for Optical and Magnetic Resonance Spectroscopy and Department of Physics, East China Normal University, Shanghai 200062, China.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 12, 2001
PubMed
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This study introduces generalized Davey-Stewartson equations for N-dimensional lattices, revealing how wave packets induce mean motion. It also presents soliton solutions for lattice wave modulations.

Area of Science:

  • Nonlinear dynamics
  • Condensed matter physics
  • Mathematical physics

Background:

  • Lattice systems exhibit complex dynamics under nonlinear modulations.
  • Understanding wave packet evolution in N-dimensional lattices is crucial for various physical phenomena.

Purpose of the Study:

  • To derive and analyze generalized nonlinear evolution equations for N-dimensional lattices.
  • To investigate the behavior of wave packets and acoustic modes in these lattice systems.
  • To explore modulational instability and soliton solutions.

Main Methods:

  • Quasidiscrete multiple-scale approach for analyzing weakly nonlinear modulations.
  • Derivation of generalized Davey-Stewartson (GDS) and Kadomtsev-Petviashvili (KP) equations.
  • Application of Hirota's bilinear transformation method for finding soliton solutions.

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Main Results:

  • The evolution of short wave packets in lattices with cubic and quartic potentials is governed by GDS equations, including mean motion effects.
  • The derived GDS equations are more general than those in water wave theory due to lattice anisotropy.
  • Generalized KP equations for long-wavelength acoustic modes in 2D and 3D lattices were presented.
  • Modulational instability of N-dimensional Stokes lattice waves was analyzed.
  • One- and two-soliton solutions for 2D GDS equations were obtained.

Conclusions:

  • The study provides a comprehensive framework for understanding nonlinear wave phenomena in N-dimensional lattices.
  • The derived GDS equations offer a more general description applicable to anisotropic lattice systems.
  • The findings pave the way for further research into soliton dynamics and wave interactions in complex lattice structures.