Third International Conference on Applications of Mathematics to Nonlinear Sciences.
Electron. J. Diff. Eqns., conf. 27 (2024), pp. 27-47.

Title: Nonlinear non-autonomous Boussinesq equations

Authors: Andrei  Ludu (Embry-Riddle Aeronautical Univ., Daytona Beach, FL, USA)
             Harihar Khanal (Embry-Riddle Aeronautical Univ., Daytona Beach, FL, USA)
             Adrian Stefan Carstea (National Institute of Physics and Nuclear Eng., Romania)
 
Abstract: 
We study solitary wave solutions for a nonlinear and non-autonomous 
Boussinesq system with initial conditions.  
Since the variable coefficients introduce distortions and modulations 
of the solution amplitudes, we implement a multiple-scale approach 
combining various modes in order to capture the coupling between the 
nonlinear evolution and the effect of the variable coefficient. 
The differential system is mapped into a solvable system of nonlinear and 
non-autonomous ODE which is integrable by recursion procedures.
We show that even in the limiting autonomous case, the multiple-scale 
approach  gives a new possibly integrable dispersionless coupled envelope 
system, which deserves further study.  We validate our theoretical results 
with numerical simulations, and we study their stability. 

Published August 20, 2024.
Math Subject Classifications: 35Q51, 35Q53, 35G50, 34E13, 93C70.
Key Words: Boussinesq; non-autonomou; nonlinear;  multiple-scale; soliton.