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

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Figure 4.14: Pulse propagating over a synthetic periodic rapid-varying topography.
Dotted line: numerical solution for the WNCM using RK4 with N= 1024 for
t=35.3429, dashed line: initial condition, solid line: flat bottom exact solution.
4.5 Computing solitary waves solutions
Now we present two examples of internal solitary waves from the Regularized
ILW equation evolving according to the WNFM. That is, we take as initial condition
for the WNFM a solitary wave from its unidirectional reduction. We expect
the wave to behave almost like a solitary wave. In particular, the balance between
nonlinearity and dispersion should be maintained and the wave should travel without
a significant change of shape. The velocity of propagation should be similar
to that in the ILW equation. The numerical solutions are obtained by the RK4
numerical solver for the WNFM withρ 1 = 1,ρ 2 = 2,β=0.0001,α=0.01,
N= 256,∆ξ=2l/N= 0.1963,l=8π,∆t=∆ξ=0.1963.
Example 4.8. In Fig. 4.15 the evolution of an approximate solitary wave solution
is shown. As initial condition forη, the parametersθ = π/8, a = −0.09953
81