Shengqiang TANG, Libing ZENG, Dahe FENG

Bifurcations and parametric representations of traveling wave solutions for the Green--Naghdi equations

By using the bifurcation theory of dynamical systems to study the dynamical behavior of the Green--Naghdi equations, the existence of solitary wave solutions along with smooth periodic traveling wave solutions is obtained. Under different regions of parametric spaces, various sufficient conditions to guarantee the existence of the above solutions are given. Some exact and explicit parametric representations of traveling wave solutions are constructed.

Anahtar Kelimeler:

Green--Naghdi equations, bifurcation theory of dynamical systems, bifurcation curves, solitary waves, periodic waves

Bifurcations and parametric representations of traveling wave solutions for the Green--Naghdi equations

Keywords:

Green--Naghdi equations, bifurcation theory of dynamical systems, bifurcation curves, solitary waves, periodic waves,

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u2(x, t) = c− g1 ϕ∗+ νM− (νM− ν2) tanh2 √ 3(νM−ν2) (x− ct) 2g (4b) The wave profiles of η2(ξ) and u(ξ) are shown in Figure 4 for c = 2, g1= 1, ϕ∗=−2.1, ν2= 762548006, ν1= 3.537451994, νM= 4.37806073, andh= 17.10947023 . 0.8 –4 –3 –2 –1 1 2 3 4 xi (a) 0.6 –10 –5 5 10 xi (b)