Real parameters for waves described by nonlinear Schrondinger equation

This information may be difficult to find on the internet, so it would be helpful if anyone could share their knowledge or experiences with solving NLS equations in the context of water waves. In summary, the dimensions of a real NLS soliton in the water wave context are dependent on local conditions and may be difficult to find information on. It would be appreciated if anyone could share their knowledge on this topic.
  • #1
hanson
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Hi all.
I know that KdV and NLS can be used to model quite a few problems.
What I am interested in is in the water wave context.
I know roughly how to solve NLS analytically and numerically, but I am just curious in real world, what is the dimension of a real NLS soliton. Say, what is the wave number? what is the water depth? what is the pulse width etc.. I can hardly find this in the internet. (perhaps my search skills is way too bad)

Can anyone share your information if you have? Thanks.
 
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  • #2
The answers to your questions depend on the particular application of the KdV and NLS equations. In the context of water waves, the dimensions of a soliton will depend on the local conditions of the wave, such as the water depth, wave number, and pulse width. The exact dimensions of a soliton can only be determined through the analysis of the particular conditions in the given environment.
 

What is the nonlinear Schrondinger equation?

The nonlinear Schrondinger equation is a mathematical equation used to describe the behavior of waves in nonlinear systems. It is a generalization of the famous Schrondinger equation and is often used in fields such as optics, fluid mechanics, and quantum mechanics.

What are real parameters for waves?

The term "real parameters" refers to physical quantities that can be measured and observed in the real world. In the context of the nonlinear Schrondinger equation, these parameters could include things like the amplitude, frequency, and velocity of a wave.

How does the nonlinear Schrondinger equation differ from the linear Schrondinger equation?

The nonlinear Schrondinger equation takes into account the effects of nonlinearity, while the linear Schrondinger equation assumes that the system is linear. This means that the nonlinear equation can describe more complex and realistic systems, while the linear equation is limited to simpler ones.

What is the significance of the nonlinear Schrondinger equation in physics?

The nonlinear Schrondinger equation is an important tool for understanding and predicting the behavior of waves in various systems. It has applications in many areas of physics, including optics, fluid dynamics, and quantum mechanics.

How are real parameters for waves determined in practice?

In most cases, real parameters for waves are determined through experiments and observations. Scientists may use instruments such as sensors, detectors, and spectrometers to measure the physical quantities associated with a wave and then use these values in the nonlinear Schrondinger equation to describe its behavior.

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