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| Shape Analysis of Bounded Traveling Wave Solutions and Solution to the Generalized Whitham-Broer-Kaup Equation with Dissipation Terms |
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Citation： |
Weiguo ZHANG,Qiang LIU,Xiang LI,Boling GUO.Shape Analysis of Bounded Traveling Wave Solutions and Solution to the Generalized Whitham-Broer-Kaup Equation with Dissipation Terms[J].Chinese Annals of Mathematics B,2012,33(2):281~308 |
| Page view： 2167
Net amount： 1612 |
Authors： |
Weiguo ZHANG; Qiang LIU; Xiang LI; Boling GUO; |
Foundation： |
the National Natural Science Foundation of China (No.11071164), the Natural Science Foundation of Shanghai (No.10ZR1420800) and the Shanghai Leading Academic Discipline Project (No.S30501). |
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| Abstract： |
This paper deals with the problem of the bounded traveling wave solutions' shape and the solution to the generalizedWhitham-Broer-Kaup equation with the dissipation terms which can be called WBK equation for short. The authors employ the theory and method of planar dynamical systems to make comprehensive qualitative analyses to the above equation satisfied by the horizontal velocity component $u(\xi)$ in the traveling wave solution $(u(\xi),H(\xi))$,
and then give its global phase portraits. The authors obtain the existent conditions and the number of the solutions by using the relations between the components $u(\xi)$ and $H(\xi)$ in the solutions. The authors study the dissipation effect on the solutions, find out a critical value $r^{*}$, and prove that the traveling wave solution $(u(\xi),H(\xi))$ appears as a kink profile solitary wave if the dissipation effect is greater, i.e., $|r|\geq r^{*}$, while it appears as a damped oscillatory wave if the dissipation effect issmaller, i.e., $|r| |
Keywords： |
Generalized Whitham-Broer-Kaup equation, Shape analysis, Solitary wave solution,Damped oscillatory solution, Error estimate |
Classification： |
35G25, 35Q35, 35Q51 |
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