Bilinear residual network method for solving the exactly explicit solutions of nonlinear evolution equations

In this work, bilinear residual network method is proposed to solve nonlinear evolution equations. The activation function in final layer of deep neural network cannot interact with the neuron inside the deep neural network, but the residual network can transfer the input layer to the activation function in final layer to realize the interaction within the network. This reduces the complexity of the model and gives more interactive results. The steps of solving the exact analytical solution through the residual network are given. The rogue wave solution of Caudrey-Dodd-Gibbon-Kotera-Sawada-like equation is obtained by using the bilinear residual network method. Characteristic plots and dynamic analysis of these rogue waves are given.

Automated summary

In this study, a bilinear residual network method is proposed to solve nonlinear evolution equations. The method reduces the complexity of the model and provides more interactive results. The exact analytical solution for the Caudrey-Dodd-Gibbon-Kotera-Sawada-like equation is obtained using the steps of solving through the residual network. Characteristic plots and dynamic analysis of these rogue waves are given.