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

0.1
0.09
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0
0 10 20 30 40 50 60
Figure 4.15: Numerical solution of the WNFM withβ=0.0001,α=0.01 for the
propagation of a single solitary wave.
andλ = 0.3323 are selected in the solitary wave solution of Eq. (2.42); u 1 is
taken to be the corresponding dispersive solution for one propagation direction,
see Section 4.3.
The expected behaviour of the wave is captured by the numerical method for
long times as shown in Fig. 4.16. The pulse propagates with an approximate
velocity of 0.9884 in conformity with its propagation velocity c=0.9961 in the
Regularized ILW equation (2.42). The shape of the solitary wave is preserved for
long times as shown in Fig. 4.17. The error between the initial condition and the
solution that returns to the original position at approximate time t=50.8545 is
0.0047. Taking into account that the choice of u 1 is an approximation from the
linear case (α=0), the result is satisfactory.
Example 4.9. In Fig. 4.18 the fission of a single approximate solitary wave solution
is simulated. As initial condition forη, the same parametersθ = π/8,
a=−0.099536 andλ=0.3323 are used, while u 10 = 0. We observe two waves
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