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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Solving Higher-Order Kinetic Energy Term (Gross-Pitaevskii equation) [closed]
Consider now propagation of non-linear waves in one-dimensional chain of dimers governed by the non-linear Schrödinger equation for the normalized wave envelope $\Psi(x,t)$,
$$
i \frac{\partial \Psi}{...
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Characteristics of wavepackets
I've been learning about wave packets and group velocities recently and had a question. Using simple trigonometric identies, we can show that the super position of two traveling waves with frequency-...
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Non-topological solitons in condensed matter physics
As I know most well-known soliton solutions in condensed matter physics are topological ones: kinks, domain walls etc.
In field theory there are several examples on non-topological solitons: Q-balls, ...
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Do plane waves exist in nature? [duplicate]
Drop a stone in the pond...a wave propagates radially from the source. The conservation of energy says the wave must decay proportionally to the radial distance. If I drop a steel I-beam in the pond, ...
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Nonlinear Saturated Schrodinger Equation in 1D- Physical Models
I'm studying the Nonlinear 1d Schrodinger equation
$$i\psi _t + \psi '' + |\psi |^{2p} \psi - \epsilon |\psi | ^{2q} \psi = 0\, , \quad t>0, x\in \mathbb{R}\, ,$$
and specifically, its solitary ...
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Can localized fluid perturbations be accelerated by pressure gradients?
I would like to know if there are any examples in fluid dynamics (or continuum dynamics) of small perturbations (or waves, solitons, or other "localized" solutions of the fluid) being accelerated in ...
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$\phi^4$ theory kinks as fermions?
In 1+1 dimensions there is duality between models of fermions and bosons called bosonization (or fermionization). For instance the sine-Gordon theory $$\mathcal{L}= \frac{1}{2}\partial_\mu \phi \...
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From the viewpoint of field theory and Derrick's theorem, what's the classical field configuration corresponding to particle? Is it a wavepacket?
In the framework of QM, we have known that particle, like electron, cannot be a wavepacket, because if it is a wavepacket then it will become "fatter" due to dispersion and it's impossible.
However ...
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Left-right topology
Are there non-trivial topological solutions (in particular 't Hooft-Polyakov magnetic monopoles) associated with the (local) breaking
\begin{equation}
SU(2)_R \times SU(2)_L \times U(1)_{B-L} \to SU(...
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Why do vortices scatter at right-angles
I have been taking a course on non-perturbative physics and currently the teacher is away so I cannot ask him.
In the lectures, he made the claim that a pair of vortices in the abelian-Higgs model ...
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Why can you make $V$ stationary with respect to a parameter of the field in Derrick's theorem?
I'm going over Coleman's derivation of Derrick's theorem for real scalar fields in the chapter Classical lumps and their quantum descendants from Aspects of Symmetry (page 194).
Theorem: Let $\phi$ ...
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Mathematical understanding of vortex solitons
I am wondering if anyone has ever come up with a mathematical description of something that (to me, and I am no expert) look like soliton vortexes.
The example I can think of is if you create two ...
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Few basic questions about instantons
For the $SU(2)$ Yang-Mill's theory, (1) how can one understand that the finite action solutions of the Euclidean equations of motion (called Instantons) exhibit tunneling effects? (2) Since, this ...
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Question from Terning's book
In Chapter 7 of Terning's book (Modern Supersymmetry), the first example considered is that of an $SO(3)$ gauge theory, a complex scalar in the triplet representation of $SO(3)$ and a potential term:
$...
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What is beam confinement?
In the context of the propagation of an electromagnetic wave and optical vortex solitons, I came across the term "beam confinement". Particularly, beam confinement requires the amplitude of the ...
