Third International Conference on Applications of Mathematics to Nonlinear Sciences.
Electron. J. Diff. Eqns., Conference 27 (2024), pp. 27-47.
Nonlinear non-autonomous Boussinesq equations
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
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Andrei Ludu
Embry-Riddle Aeronautical University
Department of Mathematics and Wave Lab
Daytona Beach, FL, USA
email: ludua@erau.edu
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Harihar Khanal
Embry-Riddle Aeronautical University
Department of Mathematics
Daytona Beach, FL, USA
email: harihar.khanal@erau.edu
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Adrian Stefan Carstea
Department of Theoretical Physics
National Institute of Physics and Nuclear Engineering
Bucharest-Magurele 077125, Romania
email: acarst@theory.nipne.ro
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