Andrei Ludu, Harihar Khanal, Adrian Stefan Carstea
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.
DOI: 10.58997/ejde.conf.27.l1
Show me the PDF file (1892 K), TEX file for this article.
 |
Andrei Ludu Embry-Riddle Aeronautical University Department of Mathematics and Wave Lab Daytona Beach, FL, USA email: ludua@erau.edu |
|---|---|
 |
Harihar Khanal Embry-Riddle Aeronautical University Department of Mathematics Daytona Beach, FL, USA email: harihar.khanal@erau.edu |
 |
Adrian Stefan Carstea Department of Theoretical Physics National Institute of Physics and Nuclear Engineering Bucharest-Magurele 077125, Romania email: acarst@theory.nipne.ro |
Return to the table of contents
for this conference.
Return to the EJDE web page