Abundant time-wavering solutions of a modified regularized long wave model using the EMSE technique

This research article presents the application of the enhanced modified simple equation integral technique to obtain abundant time-wavering solutions of the modified regularized long wave (RLW) model. The model is known for its significance in exploring wave phenomena in various fields, including shallow water dynamics, pressure waves in liquids and gas bubbles, nonlinear transverse waves in magneto-hydrodynamics, and ion-acoustic waves in plasma. By implementing the enhanced modified simple equation integral technique, we construct arbitrary time-varying wave solutions for the model, resulting in a diverse range of solitonic waveforms. These solutions include kink waves, anti-kink waves, bright and dark bell waves, double periodic waves, and combinations of solitons and periodic waves. The obtained solutions are visually presented through 2D and 3D density and contour plots. Our findings demonstrate the effectiveness and potential of the enhanced modified simple equation integral technique in identifying innovative time-varying soliton solutions within the modified RLW model.