Rosenau–Hyman equation

The Rosenau–Hyman equation or K(n,n) equation is a KdV-like equation having compacton solutions. This nonlinear partial differential equation is of the form[1]

The equation is named after Philip Rosenau and James M. Hyman, who used in their 1993 study of compactons.[2]

The K(n,n) equation has the following traveling wave solutions:

  • when a > 0
  • when a < 0

References

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  1. ^ Polyanin, Andrei D.; Zaitsev, Valentin F. (28 October 2002), Handbook of Nonlinear Partial Differential Equations (Second ed.), CRC Press, p. 891, ISBN 1584882972
  2. ^ Rosenau, Philip; Hyman, James M. (1993), "Compactons: Solitons with finite wavelength", Physical Review Letters, 70 (5), American Physical Society: 564–567, Bibcode:1993PhRvL..70..564R, doi:10.1103/PhysRevLett.70.564, PMID 10054146