All Questions
Tagged with solitons homework-and-exercises
5
questions
1
vote
0
answers
57
views
Obtaining the topological charge
I want to obtain the topological charge or winding number of the map
$$
f_n(\mathbf{r})=(\sin \theta \cos (n \varphi), \sin \theta \sin (n \varphi), \cos \theta)
$$
and my lecture notes say that it is ...
- 161
1
vote
1
answer
335
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Asymptotic behaviour of soliton-antisoliton solution for the Sine Gordon equation
The question isn't about any actual homework, it's rather a (probably simple) intermediate step I've encountered on Rajaraman's Solitons and instantons : an introduction to solitons and instantons in ...
- 150
3
votes
1
answer
899
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Finding the energy of a solution to the Sine-Gordon equation
I am delving into Quantum-Field Theory, and am stuck trying to work out how to compute the energy of a soliton solution to the Sine-Gordon equation in 1-1 spacetime.
I start with the Lagrangian ...
- 1,224
3
votes
2
answers
342
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Why is the solution of the $\phi^6$ potential not a soliton?
Consider a theory with a $\phi^6$-scalar potential:
$$
\mathcal{L} = \frac{1}{2}(\partial_\mu\phi)^2-\phi^2(\phi^2-1)^2.
$$
I solved its equation of motion but found that the general form of its ...
- 175
2
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0
answers
244
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Phase and group velocity of a soliton? [closed]
How do I find the phase velocity and group velocity of a soliton with a $\operatorname{sech}$ (hyperbolic secant) envelope?
- 151