Numerical and perturbative computations of solitary waves of the Benjamin―Ono equation with higher order nonlinearity using Christov rational basis functions
In: Journal of computational physics (Print), Jg. 231 (2012), Heft 4, S. 1216-1229
academicJournal
- print, 44 ref
Zugriff:
Computation of solitons of the cubically-nonlinear Benjamin-Ono equation is challenging. First, the equation contains the Hilbert transform, a nonlocal integral operator. Second, its solitary waves decay only as O(1/|x|2). To solve the integro-differential equation for waves traveling at a phase speed c, we introduced the artificial homotopy H(uxx) ― c u + (1 ― δ)u2 + δu3 = 0, δ ∈ [0,1] and solved it in two ways. The first was continuation in the homotopy parameter δ, marching from the known Benjamin-Ono soliton for δ = 0 to the cubically-nonlinear soliton at δ = 1. The second strategy was to bypass continuation by numerically computing perturbation series in δ and forming Padé approximants to obtain a very accurate approximation at δ = 1. To further minimize computations, we derived an elementary theorem to reduce the two-parameter soliton family to a parameter-free function, the soliton symmetric about the origin with unit phase speed. Solitons for higher order Benjamin-Ono equations are also computed and compared to their Korteweg-deVries counterparts. All computations applied the pseudospectral method with a basis of rational orthogonal functions invented by Christov, which are eigenfunctions of the Hilbert transform.
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Numerical and perturbative computations of solitary waves of the Benjamin―Ono equation with higher order nonlinearity using Christov rational basis functions
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Autor/in / Beteiligte Person: | BOYD, John P ; ZHENGJIE, XU |
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Zeitschrift: | Journal of computational physics (Print), Jg. 231 (2012), Heft 4, S. 1216-1229 |
Veröffentlichung: | Kidlington: Elsevier, 2012 |
Medientyp: | academicJournal |
Umfang: | print, 44 ref |
ISSN: | 0021-9991 (print) |
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