Weakly nonlinear waves in water of variable depth: Variable-coefficient Korteweg-de Vries equation
Citation
Demiray, H. (2010). Weakly nonlinear waves in water of variable depth: Variable-coefficient Korteweg–de vries equation. Computers and Mathematics with Applications, 60(6), 1747-1755. doi:10.1016/j.camwa.2010.07.005Abstract
In the present work, utilizing the two-dimensional equations of an incompressible inviscid fluid and the reductive perturbation method, we studied the propagation of weakly non-linear waves in water of variable depth. For the case of slowly varying depth, the evolution equation is obtained as a variable-coefficient Korteweg-de Vries (KdV) equation. A progressive wave type of solution, which satisfies the evolution equation in the integral sense but not point by point, is presented. The resulting solution is numerically evaluated for two selected bottom profile functions, and it is observed that the wave amplitude increases but the band width of the solitary wave decreases with increasing undulation of the bottom profile.
Source
Computers and Mathematics with ApplicationsVolume
60Issue
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