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Original Articles

A modified explicit numerical scheme for the two-dimensional sine-Gordon equation

Pages 241-252 | Received 17 Feb 2006, Accepted 24 Apr 2007, Published online: 02 Oct 2008

References

  • Ablowitz , M. J. and Segur , H. 1981 . Solitons and the Inverse Scattering Transforms , Philadelphia, PA : SIAM .
  • Lamb , G. L. 1980 . Elements of Soliton Theory , New York : Wiley .
  • Hirota , R. 1973 . Exact three-soliton solution of the two-dimensional sine-Gordon equation . Journal of the Physical Society of Japan , 35 : 1566
  • Kobayashi , K. K. and Izutsu , M. 1976 . Exact solution of the n-dimensional sine-Gordon equation . Journal of the Physical Society of Japan , 41 : 1091
  • Zagrodzinsky , J. 1979 . Particular solutions of the sine-Gordon equation in 2+1 dimensions . Physics Letters A , 72 : 284 – 286 .
  • Leibbrandt , G. 1978 . New exact solutions of the classical sine-Gordon equation in 2+1 and 3+1 dimensions . Physical Review Letters , 41 : 435 – 438 .
  • Kaliappan , P. and Lakshmanan , M. 1979 . Kadomtsev–Petviashvili and two-dimensional sine-Gordon equations: reduction to Painlevé transcendents . Journal of Physics A: Mathematics General , 12 : 249
  • Christiansen , P. L. and Lomdahl , P. S. 1981 . Numerical solutions of 2+1 dimensional sine-Gordon solitons . Physica D: Nonlinear Phenomena , : 482 – 494 .
  • Argyris , J. , Haase , M. and Heinrich , J. C. 1991 . Finite element approximation to two-dimensional sine-Gordon solitons . Computer Methods in Applied Mechanics and Engineering , 86 : 1 – 26 .
  • Bratsos , A. G. 2005 . An explicit numerical scheme for the sine-Gordon equation in 2+1 dimensions . Applied Numerical Analysis and Computational Mathematics , 2 : 189 – 211 .
  • Nakajima , K. , Onodera , Y. , Nakamura , T. and Sato , R. 1974 . Numerical analysis of vortex motion on Josephson structures . Journal of Applied Physics , 45 : 4095 – 4099 .
  • Djidjeli , K. , Price , W. G. and Twizell , E. H. 1995 . Numerical solutions of a damped sine-Gordon equation in two space variables . Journal of Engineering Mathematics , 29 : 347 – 369 .
  • Bogolyubski , I. L. and Makhankov , V. G. 1976 . Lifetime of pulsating solitons in certain classical models . Journal of Experimental and Theoretical Physics Letters (Pis'ma v Zhurnal Eksperiment'noi i Teoreticheskoi Fiziki ) , 24 ( 1 ) : 12 – 14 .
  • Bogolyubski , I. L. 1976 . Oscillating particle-like solutions of the nonlinear Klein-Gordon equation . Journal of Experimental and Theoretical Physics Letters (Pis'ma v Zhurnal Eksperiment'noi i Teoreticheskoi Fiziki) , 24 : 535 – 538 .

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