Faculty Mentor(s)

Dr. Ramjee Sharma

Campus

Gainesville

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 𝑒𝑑+π‘Žπ‘’π‘₯+2𝑏𝑒𝑒π‘₯+𝑐𝑒π‘₯π‘₯π‘₯βˆ’π‘‘π‘’π‘₯π‘₯=0.

The above equation is the generalized version of the KDV equation 𝑒𝑑+𝑒π‘₯+2𝑒𝑒π‘₯+𝛿𝑒π‘₯π‘₯π‘₯=0.

Here 𝑒=𝑒(π‘₯,𝑑) is a scalar function of π‘₯βˆˆπ‘…and 𝑑β‰₯0, while 𝛿>0 is a parameter. This equation is used to model the unidirectional propagation of water waves. The scalar 𝑒represents 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‘Ž,𝑏,𝑐 and 𝑑 tend to zero. This is carried out through numerical computations using the pseudo-spectral method.

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Mar 23rd, 9:00 AM Mar 23rd, 10:00 AM

Numerical Computations of Generalized Korteweg-de Vries (KdV) equations

Nesbitt 3203

We consider the following generalized Korteweg-deVries (KdV) equation 𝑒𝑑+π‘Žπ‘’π‘₯+2𝑏𝑒𝑒π‘₯+𝑐𝑒π‘₯π‘₯π‘₯βˆ’π‘‘π‘’π‘₯π‘₯=0.

The above equation is the generalized version of the KDV equation 𝑒𝑑+𝑒π‘₯+2𝑒𝑒π‘₯+𝛿𝑒π‘₯π‘₯π‘₯=0.

Here 𝑒=𝑒(π‘₯,𝑑) is a scalar function of π‘₯βˆˆπ‘…and 𝑑β‰₯0, while 𝛿>0 is a parameter. This equation is used to model the unidirectional propagation of water waves. The scalar 𝑒represents 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‘Ž,𝑏,𝑐 and 𝑑 tend to zero. This is carried out through numerical computations using the pseudo-spectral method.