Abstract
We consider the following generalized Korteweg-deVries (KdV) equation π’π‘+ππ’π₯+2ππ’π’π₯+ππ’π₯π₯π₯βππ’π₯π₯=0.
The above equation is the generalized version of the KDV equation π’π‘+π’π₯+2π’π’π₯+πΏπ’π₯π₯π₯=0.
Here π’=π’(π₯,π‘) is a scalar function of π₯βπ and π‘β₯0, while πΏ>0 is a parameter. This equation is used to model the unidirectional propagation of water waves. The scalar π’represents the amplitude of the wave.
In this presentation we investigate the various limits of the solutions of the generalized equation as one or more of the parameters as π,π,π and π tend to zero. This is carried out through numerical computations using the pseudo-spectral method.
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Metadata
- Subject
Mathematics
- Institution
Gainesville
- Event location
Nesbitt 3203
- Event date
23 March 2018
- Date submitted
19 July 2022
- Additional information
Acknowledgements:
Dr. Ramjee Sharma