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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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 ...
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What does topologically stable mean?

I am working on an article about skyrmion manipulation and it is written that those particles are "topologically stable particle-like spin configurations that carry a characteristic topological charge ...
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How does the $U(1)$ global symmetry break in the gauged $XY$ model?

I'm studying the particle vortex duality, and I'm confused how we're able to say that in the Coulomb phase, the "hidden" $U(1)$ global magnetic symmetry spontaneously breaks. gauged XY model: $\...
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Is Brandt-Neri-Coleman stability analysis valid?

My question is related to the problem of stability of magnetic monopoles in Yang-Mills-Higgs theories. I have read "The Magnetic Monopole 50 years later" from Coleman and, in section 3.5, he discusses ...
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Will tsunami waves travel forever if there was no land?

If there was no land for tsunami waves to collide with, can the waves travel around the globe for forever?
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How solitons are related to particle physics?

Recently, I read a paper about introduction to solitons. Author said that the solutions of sine-Gordon equation can be candidate for modeling elementary particles and there are some applications in ...
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Different between droplet and a soliton

I am working on the droplet state in a Bose-Bose mixture. I have a question about the difference between the droplet liquid state and the soliton state: How we can treat a droplet state? And how do we ...
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Why do we consider solitons as a composite object?

Can someone explain why do we consider solitons as a composite object? I know that there are dual theories which the role of fundamental and solitonic objects can be mapped to each other, but I can't ...
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Can inhomogeneity in the medium accelerate particles

Suppose I have a charge which is moving in through a medium with constant velocity. Now, what will happen to the charge as it encounters an inhomogeneity in density? whether it will accelerate or ...
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What does the motion of water in tsunamis look like?

This is what normal wave motion looks like. Do tsunamis that travel at 60mph look any different?
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Photon number in optics

What does the term, photon number, mean in optics? I came across the term in research papers on squeezed light. One such line in a research paper reads: Quantum solitons consist of linear ...
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Topological solitons in general dimension

Let's begin with a simple model of a field theory: $$ \mathcal{H} = \int ( \nabla \phi ) ^2 $$ where $\phi$ is an angle valued field defined on some space. We suppose for the moment to freeze out ...
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Topological properties of dark solitons in superfluid systems

In the study of superfluid systems, vortices are often referred to as "topological excitations", because the winding of the phase of the superfluid order parameter around a vortex is a topological ...
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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 ...
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How to use Belinsky-Zakharov transformation

I know it might be trivial. When using BZ transformation [1] to generate soliton solutions of Einstein’s field equations, one need a seed solution $g_{0}$ which gives $A_{0}$ and $B_{0}$. Taking them ...
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155 views

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 ...
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63 views

Violation of Derrick's theorem for finite energy, time independent solutions?

How are vortices the finite energy time independent solutions for 2+1 dimensions abelian higgs model? Doesn't it violate derricks theorem that there are no finite energy time independent solutions in ...
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Non-chiral skyrmion v.s. Left/Right chiral skyrmion

A skyrmion in a 3-dimensional space (or a 3-dimensional spacetime) is detected by a topological index $$n= {\tfrac{1}{4\pi}}\int\mathbf{M}\cdot\left(\frac{\partial \mathbf{M}}{\partial x}\times\frac{...
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Are static black holes solitons?

If we start with the Einstein-Hilbert action with no matter, and consider time independent finite energy field configurations, then any static solution (e.g Schwarzchild metric) seems to be a soliton-...
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478 views

What is the intuition for topological currents?

The reason for topological stability of a kink solution in scalar field theory in $1+1$ dimensions is the fact that the finite energy scalar field cannot be continuously deformed into a vacuum. How ...
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KdV suggests a connection between waves in shallow water and the potential in the Schrödinger equation. What is the intuitive explanation?

The KdV equation $$v_t+\frac{1}{4}v_{xxx}-\frac{3}{2}vv_x=0$$ was originally invented to model waves in shallow water. However, it is well known that it also has applications in quantum mechanics. ...
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M branes/D branes are solitons?

I'm really confused. In M theory/String theory, the fundamental objects are M/D branes. However, branes by defintion are just solitons. Solitons are just waves that maintain there shape. So if a ...
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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 $\...
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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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276 views

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 ...