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Numerical stability of the KdV equation with a negative forcing
Author(s) -
Whang Sungim,
Choi Jeongwhan
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200701080
Subject(s) - froude number , korteweg–de vries equation , inviscid flow , forcing (mathematics) , compressibility , stability (learning theory) , mathematical analysis , mathematics , domain (mathematical analysis) , physics , mechanics , classical mechanics , nonlinear system , breakup , quantum mechanics , machine learning , computer science
The waves at the free surface waves of an incompressible and inviscid fluid in a two dimensional domain with horizontal rigid flat bottom with a small obstruction are considered. A time dependent KdV equation with a negative forcing is derived and studied both theoretically and numerically. The existence of a negative solitary‐wave‐like solution of the equation near the Froude number is proved and the numerical stability of the solution is also studied. The numerical stability of the positive both symmetric and unsymmetric solitary‐wave‐like solutions are also studied. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)