## 3 Results of Numerical Simulation
As can be seen from Figure 4, the effect of slowing the decay of the average intensity is noticeable already at distances of 5-7 km from the source, and to a distance of 30 km it can exceed 60 dB. The significant effect in this waveguide compared with the previous ones is due to stronger fluctuations of the modal  
Figure 3: Similarly Figure 2 transmission loss for a waveguide with Gaussian fluctuations, \(L_{z}=20\) m, \(L_{r}=4\) km, and parameters of the bottom: \(c_{1}=1530\) m/s, (\(\rho_{1}/\rho_{0}\)) = 1.5, \(\beta_{1}=0.01\). \(H\)-\(z_{0}=42\) m. Blue curves: \(H\)-\(z=42\) m. Red curves: \(H\)-\(z=26\) m. Thin dash curves correspond to the adiabatic approximation, thick dash curves represent a deterministic waveguide (\(\varepsilon=0\)). wave numbers \(\kappa_{m}\). The consequence of this is the rapid development of strong fluctuations of the intensity of the sound field, which on average reduces the transmission losses. Let us now compare the simulation results for waveguides with Gaussian statistics of fluctuations \(\varepsilon(r,z)\), presented above, with results for similar waveguides, but having non-Gaussian fluctuations \(\varepsilon\). Consider random fields of the form:  
\[\varepsilon(r,z)=\varepsilon_{1}(z)\ \varepsilon_{2}(r),\ \ \ \ \ |\varepsilon(r,z)|<<1, \tag{14}\]  
where \(\varepsilon_{1}(z)\) is Gaussian random process and \(\varepsilon_{2}(r)\) is non-Gaussian one. These processes are statistically independent and have the same correlation function as before: \(B_{\varepsilon}(r_{1}-r_{2},z_{1}-z_{2})=\sigma_{\varepsilon}^{2}exp(-\frac {|r_{1}-r_{2}|}{L_{\varepsilon}}-\frac{|z_{1}-z_{2}|}{L_{\varepsilon}})\), \(\sigma_{\varepsilon}^{2}=\sigma_{1}^{2}\sigma_{2}^{2}\). One of the well-known non-Gaussian random processes is the telegraph process, which is widely used in various fields of economics, mathematics, physics, and optics [33]. For the description of random perturbations in underwater acoustics, the telegraph process was not widespread, but it can serve as a model of weak nonlinear cnoidal waves having a discontinuous amplitude, which are often present in the composition of background internal waves on the sea shelf. This process is defined as follows: \(\varepsilon_{2}(r)=\sigma_{2}(-1)^{n(0,r)}\), where \(n(0,r)\) is the Poissonian random process with a probability distribution \(P_{n(r1,r2)=n}=\langle n(r_{1},r_{2})\rangle^{n}\ exp[-\langle n(r_{1},r_{2}) \rangle]/n!\), where \(\langle n(r_{1},r_{2})\rangle\) is the average number of points on the interval \((r_{1},r_{2})\), \(\langle n(r_{1},r_{2})\rangle=\
u|r_{1}-r_{2}|\). If at \(r=0\), \(\varepsilon_{2}(0)=\pm\sigma_{2}\) is equiprobable, then \(\varepsilon_{2}(r)\) is a stationary process, having the average \(\langle\varepsilon_{2}(r)\rangle=0\), and the correlation function \(B_{\varepsilon_{2}}(r_{1}-r_{2})=\sigma_{2}^{2}exp(-|r_{1}-r_{2}|/L_{r})\), \(L_{r}=(2\
u)^{-1}\). In Figure 5 for two horizons, the transmission losses are presented in a waveguide with Gaussian fluctuations, as in Figure 3, and with fluctuations of the form (14) using the telegraph random process \(\varepsilon_{2}(r)\) described above. It is clearly seen that the telegraph process noticeably underlines the weakening of the decay of the average intensity in the waveguide. The corresponding curves begin to diverge at \(r>8\)-10 km, and the loss attenuation to 30 km, caused by the difference in the fluctuation field from the Gaussian one, is 10 dB or more. In this case, the curves become somewhat more cut due to the discontinuous nature of the telegraph process \(\varepsilon_{2}(r)\). For a waveguide with a \"soft bottom\" (Figure 6),  
Figure 4: Similarly Figure 3 transmission loss for a waveguide with Gaussian fluctuations, \(L_{z}=20\) m, \(L_{r}=4\) km, and parameters of the bottom \(c_{1}=1200\) m/s, \((\rho_{1}/\rho_{0})=1.5\), \(\beta_{1}=0.01\).