Questions tagged [solitons]
Solitons are self-stabilizing solitary wave packets maintaining their shape propagating at a constant velocity. They are caused by a balance of nonlinear and dispersive (where the speed of the waves varies with frequency) effects in the medium.
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Is transition between field configurations a tunneling process?
I'm considering D=1+1 kink solution here.
Given a D=2 theory with $\mathbb{Z}_2$ symmetry, there are 4 different mappings (or 2 distinct sectors---trivial and kink) from spacetime manifold (or just a ...
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Applications of Optical Solitons
It is well known for the past 50-60 years that intense laser beams can form into soliton/solitary waves. Those exist either spatially in CW beams or temporally in ultra-short pulses, and their ...
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Do solitons in QFT really exist? [closed]
In general, solitons are single-crest waves which travel at constant speed and don't loose their shape (due to their non-dispersivity), and there are many examples of them in the real world.
Now in ...
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Why does this condition guarantees there exists only a finite number of discrete energy levels?
I'm reading section 2.2.1 of the book Solitons, Instantons and Twistors by Maciej Dunajski. The section is on the subject of direct scattering.
It is claimed that, considering Schrodinger's equation ...
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Gauge potential over $\mathbb{S}^4$ vs. $\mathbb{R}^4$
NICHOLAS MANTON in "Topological Solitons" says
"One may also regard the gauge potential as a connection on an $SU(2)$
bundle over $\mathbb{S}^4$, with field strength $F$. The fact that we can ...
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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 ...
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Are there general Soliton-Instanton correspondence?
In the symmetric double well potential, the solutions in $1+1$ static and real $\varphi^4$ theory, are solitons. However, we know that such theories are "dual" to one dimensional real $\varphi^4$ ...
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Systems with 'many' conserved quantities
The classical justification for the microcanonical ensemble relies on the fact that most many-body systems have just a 'small' (typically finite) number of conserved quantities (i.e. they violate ...
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Can massive particles be seen as soliton solutions?
I wonder if the common relativistic wave equations contain a sort of soliton solutions, which might be considered as particle localisations.
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Toda lattice solution for different algebras
It is well-known that Toda systems (Toda field theory) can possess different algebraic structure based on Cartan Matrix in the Hamiltonian's potential.
But all solutions I have seen were written only ...
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Boundary condition for solitons in 1+1 dimensions to have finite energy
Suppose a classical field configuration of a real scalar field $\phi(x,t)$, in $1+1$ dimensions, has the energy $$E[\phi]=\int\limits_{-\infty}^{+\infty} dx\, \left[\frac{1}{2}\left(\frac{\partial\phi}...
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Vacuum Manifold of an $SU(2)$ Theory
I am reading Coleman's book "Aspects of Symmetry", specifically chapter 6 "Classical Lumps and their Quantum Descendants". He gives an Example 5 p. 209 for the topological solutions for an $SU(2)$ ...
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How is the velocity of a soliton defined?
The equation of motion of a real scalar field $\phi(x,t)$ in 1+1 dimension in an arbitrary potential $V(\phi)$ is given by $$\frac{\partial^2\phi}{\partial t^2}-\frac{\partial^2\phi}{\partial x^2}+\...
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Describing travelling waves carrying energy from one point to another
A simple harmonic wave in one-dimension (for simplicity) $y(x,t)=A\sin(\omega t-kx)$ in a medium is often presented as an example of a travelling wave. But such a plane wave is infinitely extended ...
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What is the definition of soliton?
What is the definition of soliton? I've encountered this name in different situations like when the topic discussed is about QFT, fluid dynamics or optics, but I cannot find a general definition. I've ...
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