Literature on the Benjamin-Ono equation

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In summary, the conversation is about someone looking for introductory literature on the Benjamin-Ono equation and someone else recommending a book that has a chapter on it. However, the person seeking the recommendation is having trouble accessing the chapter and is advised to ask their university library or math department for help.
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Wuberdall
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Thank you jedishrfu,

I can't seem to get access to this chapter. I believe it is my university that haven't bought the subscription to the journal Mathematics in Science and Engineering.
 
  • #4
You might be able to get your library to do it or ask around the math dept and someone may be able to get it for you.
 

1. What is the Benjamin-Ono equation?

The Benjamin-Ono equation is a nonlinear partial differential equation that is used to model internal waves in a stratified fluid. It was first introduced in 1967 by J. L. Benjamin and G. B. Whitham, and later refined by T. Benjamin and J. Ono in 1972. It is a generalization of the Korteweg-de Vries equation, and is also known as the B-O equation or the Benjamin-Ono-Zakharov-Kuznetsov equation.

2. What are the applications of the Benjamin-Ono equation?

The Benjamin-Ono equation has applications in various fields, including fluid dynamics, oceanography, plasma physics, and nonlinear optics. It is used to study internal waves in the ocean, the behavior of plasma in tokamaks, and the propagation of electromagnetic waves in nonlinear media.

3. What are the key properties of the Benjamin-Ono equation?

The Benjamin-Ono equation is a completely integrable system, which means that it has an infinite number of conserved quantities and can be solved exactly. It also exhibits soliton solutions, which are localized waves that maintain their shape and speed during propagation. Additionally, the equation has a Hamiltonian structure and can be derived from a Lagrangian function.

4. How is the Benjamin-Ono equation solved?

The Benjamin-Ono equation can be solved using various methods, including the inverse scattering transform, the Hirota bilinear method, and the Darboux transformation. These techniques allow for the construction of exact solutions in terms of solitons and other special functions. Numerical methods, such as finite difference and spectral methods, can also be used to approximate solutions.

5. What are the current research areas related to the Benjamin-Ono equation?

Current research on the Benjamin-Ono equation focuses on several areas, such as the study of the stability and dynamics of solitons, the behavior of rogue waves, and the effects of dissipation and dispersion. Other areas of interest include the development of new numerical methods for solving the equation, as well as its applications in other fields, such as biophysics and optics.

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