Localized nonlinear waves on spatio-temporally controllable backgrounds for a (3+1)-dimensional Kadomtsev-Petviashvili-Boussinesq model in water waves

Physics of nonlinear waves on variable backgrounds and the relevant mathematical analysis continues to be the challenging aspect of the study. In this work, we consider a (3+1)-dimensional nonlinear model describing the dynamics of water waves and construct nonlinear wave solutions on spatio-temporally controllable backgrounds for the first time by using a simple mathematical tool auto-Backlund trans-formation. Mainly, we unravel physically interesting features to control and manipulate the dynamics of nonlinear waves through the background. Adapting an exponential function and general polynomial of degree two as initial seed solutions, we construct single kink-soliton and rogue wave, respectively. We choose arbitrary periodic, localized and combined wave backgrounds by incorporating Jacobi elliptic functions and investigate the modulation of these two nonlinear waves with a clear analysis and graphi-cal demonstrations. The solutions derived in this work give us sufficient freedom to generate exotic non-linear coherent structures on variable backgrounds and open up an interesting direction to explore the dynamics of various other nonlinear waves propagating through inhomogeneous media. (c) 2021 Elsevier Ltd. All rights reserved.

Automated summary

This work studies the physics and mathematical analysis of nonlinear waves on variable backgrounds. By using the auto-Backlund transformation, the authors construct nonlinear wave solutions on spatio-temporally controllable backgrounds for the first time. The study reveals physically interesting features and the ability to control and manipulate the dynamics of nonlinear waves through the background. Single kink-soliton and rogue wave solutions are constructed using different initial seed solutions, and the modulation of these two nonlinear waves on various backgrounds is investigated using Jacobi elliptic functions.