All Questions
5
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Do you know about any book which discusses solitons in Benjamin-Ono Equation?
Benjamin-Ono equation is an integrable equation with soliton solutions. There are many books on solitons. The ones I know about mainly discuss solitons in Korteweg de-Vries and related equations. Do ...
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1
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Doubt on Lax formulation of Korteweg–de Vries equation
The Korteweg–de Vries equation is given by:
$$\frac{\partial u(x,t)}{\partial t}-6u\frac{\partial u(x,t)}{\partial x}+\frac{\partial^3 u(x,t)}{\partial x^3}=0$$
This equation can be formulated using ...
- 605
1
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1
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Intuition behind focusing vs defocusing in integrable systems like NLS, KdV, mKdV
The following are examples of integrable systems arising from the AKNS system (check out AKNS paper here and a short Wikipedia description)
Non-Linear Schrodinger equation
Korteweg-de Vries equation
...
- 11
6
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3
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525
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Link between integrability and soliton solutions
I have been doing some research on the properties and dynamics of solitons (in particular, solitons in superfluids) and several works and papers mention the link between solitonic solutions and ...
- 73
2
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KdV equation and classical linear wave equation
Like we know, the standard form of KdV equation is
$$u_{t}-6uu_{x}+u_{xxx}=0,\tag{1}$$
where this equation describes a solitary wave propagation and $u=u(x,t)$.
On the other hand, we know the ...
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