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Kink dynamics in one-dimensional nonlinear systems

Author

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  • Kawasaki, Kyozi
  • Ohta, Takao

Abstract

A certain class of nonlinear evolution equations of one space dimension which permits kink type solutions and includes one-dimensional time-dependent Ginzburg-Landau (TDGL) equations and certain nonlinear wave equations is studied in some strong coupling approximation where the problem can be reduced to the study of kink dynamics. A detailed study is presented for the case of TDGL equation with possible applications to the late stage kinetics of order-disorer phase transitions and spinodal decompositions. A special case of kink dynamics of nonlinear wave equations is found to reduce to the Toda lattice dynamics. A new conservation law for dissipative systems is found which corresponds to the momentum conservation law for wave equations.

Suggested Citation

  • Kawasaki, Kyozi & Ohta, Takao, 1982. "Kink dynamics in one-dimensional nonlinear systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 116(3), pages 573-593.
    • Handle: RePEc:eee:phsmap:v:116:y:1982:i:3:p:573-593
    DOI: 10.1016/0378-4371(82)90178-9
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    Cited by:

    1. Amann, Andreas & Schöll, Eckehard & Just, Wolfram, 2007. "Some basic remarks on eigenmode expansions of time-delay dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 373(C), pages 191-202.
    2. Jara-Schulz, Gladys & Ferré, Michel A. & Falcón, Claudio & Clerc, Marcel G., 2020. "Noise-induced kink propagation in shallow granular layers," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).

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