This paper considers a fourth-order time-fractional partial differential equation with Riemann–Liouville definition. We first use the general method of separation of variables to transform the original equation into an ordinary differential equation and subsequently apply the trial equation method to obtain its integral form. The complete discrimination system for polynomial method(CDSPM) is also adopted herein. By applying this method, dynamic properties such as phase portraits are determined. The results suggest that the soliton solution coexists with the periodic solution as long as the homoclinic orbits exist. Moreover, to directly show our conclusions, the corresponding exact solutions to this equation are presented using this method.

In this paper, analytic solutions and dynamic properties of a variety of Boussinesq-type equations are established via the complete discrimination system for polynomial method. All the existing single traveling wave solutions to these equations as well as some new solutions are shown, and the Hamiltonian and topological properties to these equations are also presented. Considering the significance of the Boussinesq-type equations, our results would have wide applications in ocean engineering and fluid mechanics, like describing and predicting the solitary and periodic waves in various shallow water models.

Arterial blood pressure is not only an important index that must be measured in routine physical examination but also a key monitoring parameter of the cardiovascular system in cardiac surgery, drug testing, and intensive care. To improve the measurement accuracy of continuous blood pressure, this paper uses photoplethysmography (PPG) signals to estimate diastolic blood pressure and systolic blood pressure based on ensemble empirical mode decomposition (EEMD) and temporal convolutional network (TCN). In this method, the clean PPG signal is decomposed by EEMD to obtain n-order intrinsic mode functions (IMF), and then the IMF and the original PPG are input into the constructed TCN neural network model, and the results are output. The results show that TCN has better performance than CNN, CNN-LSTM, and CNN-GRU. Using the data added with IMF, the results of the above neural network model are better than those of the model with only PPG as input, in which the systolic blood pressure (SBP) and diastolic blood pressure (DBP) results of EEMD-TCN are −1.55 ± 9.92 mmHg and 0.41 ± 4.86 mmHg. According to the estimation results, DBP meets the requirements of the AAMI standard, BHS evaluates it as Grade A, SD of SBP is close to the standard AAMI, and BHS evaluates it as Grade B.