Faculty Mentor(s)
Dr. Ramjee Sharma
Campus
Gainesville
Proposal Type
Presentation - completed/ongoing
Subject Area
Mathematics
Location
Nesbitt 3203
Start Date
23-3-2018 9:00 AM
End Date
23-3-2018 10:00 AM
Description/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.
Numerical Computations of Generalized Korteweg-de Vries (KdV) equations
Nesbitt 3203
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.