a reduced model for internal waves interacting with submarine ...

0.6
0.4
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η
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−0.2
60
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t
10
0
0 10 20 30 40 50 60
ξ
Figure 4.5: Fission of the wave on a periodic domainΠ[0, 16π].
and the amplitude is half of the original one, see Fig. (4.5). This is consistent
with D’Alembert’s solution for the wave equation. When the two travelling waves
coincide (overlap) in space and time the initial condition is recovered with an
error of 0.00374 by the RK4 method with N = 512,∆ξ = 2l/N = 0.098175,
∆t = ∆ξ = 0.098175, see Fig. 4.6. This is a nice consistency check for the
numerical conservation of mass of two waves colliding.
Example 4.3. Let us study the numerical solutions for the LFM for the dispersive
caseβ0. The initial value problem for this case can be solved explicitly by
means of Fourier Series as follows.
Consider the initial value problem (IVP) for the LFM on the periodic domain
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