Numerical computation of solitary waves in infinite cylindrical domains

Gabriel J. Lord, Daniela Peterhof, Björn Sandstede, Arnd Scheel

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29 Scopus citations


The numerical computation of solitary waves to semilinear elliptic equations in infinite cylindrical domains is investigated. Rather than solving on the infinite cylinder, the equation is approximated by a boundary-value problem on a finite cylinder. Convergence and stability results for this approach are given. It is also shown that Galerkin approximations can be used to compute solitary waves of the elliptic problem on the finite cylinder. In addition, it is demonstrated that the aforementioned procedures simplify in cases where the elliptic equation admits an additional reversibility structure. Finally, the theoretical predictions are compared with numerical computations. In particular, post buckling of an infinitely long cylindrical shell under axial compression is considered; it is shown numerically that, for a fixed spatial truncation, the error in the truncation scales with the length of the cylinder as predicted theoretically.

Original languageEnglish (US)
Pages (from-to)1420-1454
Number of pages35
JournalSIAM Journal on Numerical Analysis
Issue number5
StatePublished - 2000


  • Boundary-value problem
  • Elliptic equation
  • Solitary-wave


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