#### 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.