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Transition bifurcation branches in non‐linear water waves
Author(s) -
Toro E. F.
Publication year - 1986
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1650060404
Subject(s) - bifurcation , bifurcation diagram , mathematics , saddle node bifurcation , transcritical bifurcation , disjoint sets , homoclinic bifurcation , infinite period bifurcation , amplitude , monotonic function , computation , mathematical analysis , geometry , physics , nonlinear system , optics , quantum mechanics , algorithm
We are concerned with the numerical computation of progressive free surface gravity waves on a horizontal bed. They are regarded as families of bifurcation branches (λ, A ) Q of constant discharge Q. Numerically we determine two transition values Q 1 and Q 2 with corresponding transition bifurcation branches that classify waves into three disjoint branch sets B 1 , B 2 and B 3 . Their members are families of waves (λ, A ) Q satisfying the conditions 0< Q 2 ⩽ Q 1 2 , Q 1 2< Q 2 ⩽ Q 2 2and Q 2 2< Q 2