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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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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An interesting observation: Ordered, up and down movement of vortex rings in water

I was watching a video on David Tong's research work when I stumbled upon a peculiar movement of vortex rings in water. Around the 1:20 time mark, Baths and Quarks: Solitons explained, David Tong uses ...
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Are QFT solitons expected to represent standard model particles? Or strings?

Is work on solitons in QFT's focused on finding solutions that could represent the fundamental particles of the Standard Model, or is the work focused on finding particles Beyond The Standard Model? ...
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Spin of skyrmion

Baryons can be considered as solitions in Skyrme model(See also this post.): Such Lagrangian haven't any information about number of colors. Bosonic or fermionic nature of baryons depends on number ...
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Intuition about ADHM construction

I'm trying to understand reasons, why self-dual Yang-Mills equation can be reduced to algebraic equations. It's seem like a miracle. In article Construction of Instanton and Monopole Solutions and ...
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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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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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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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187 views

Asymptotic limit of the two kink solution of the sine-gordon equation

I am reading a paper on the sine-gordon model. The solution for a two kink solution is given as: $$\phi=4\arctan\left(\frac{\sinh\frac{1}{2}(\theta_1-\theta_2)}{(a_{12})^\frac{1}{2}\cosh\frac{1}{2}(\...
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Completely Integrable Frustrated Lattice Systems

The Toda lattice is a prime example of a lattice system that is completely integrable, in the sense that it admits a Lax pair, https://doi.org/10.1143/PTP.51.703, making it easy to find soliton ...
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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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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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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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Categorization of electromagnetic solitons?

I've seen over the years several mentions of electromagnetic solitons that appear in the high-intensity regime (where vacuum polarization becomes important). Some of these are coupled with plasmas, ...
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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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Fractional quantum number induced in a soliton profile

It has been known there is fractional quantum number induced in a soliton profile, such as this Jeffrey Goldstone and Frank Wilczek paper and many works of Jackiw. For example the electric charge ...
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Quantum solitons: derivation of $ \int {\phi^\prime}^2 dx = M$ using Lorentz invariance

I was reading through page 10 of this document (Chua, 2017) on quantum solitons, and came across the following statement relating to the equation for kinetic energy $$T = \left(\frac{da}{dt}\right)^2\...
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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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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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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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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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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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256 views

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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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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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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111 views

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 ...
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Sine integral as a soliton profile?

Among the most commonly known 1+1 soliton/solitary-wave profiles are: $\tan^{-1}(\exp(x-vt))$ for Sine-Gordon, $\tanh(x-vt)$ for $\phi^4$, $\operatorname{sech}^2(x-vt)$ for KdV. My question is: ...
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Are there resources for simulating and/or theoretically describing solitons?

Recently there are striking new ideas emerging on "lower level" dynamics with respect to quantum mechanics involving fluid mechanics principles, including hints of soliton-like aspects to particle ...
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Is there a consensus on the definition of wavelength for a solitary wave?

Solitary waves are by definition a wave of single nature so the usual definition for periodic waves does not apply. R. Dalrymple provides a definition but I saw a lot of other websites and papers ...
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610 views

Domain wall and kink solutions from solitions equations

A general solition equation can be obtaion from scalar field theory $$\varphi(x) = v\tanh\Bigl(\tfrac{1}{2}m(x - x_0)\Bigr),\tag{92.6}$$ where $x_0$ is a constant of integration when we drived this ...
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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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Boundary conditions for radial solution of gauged topological vortices

I am following the book Topological Solitons by Manton and Sutcliffe and I am struggling to understand a boundary condition they choose to find the radial solutions of gauged vortices with finite ...
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Peak splitting in one-component reaction–diffusion equations

I am studying a one-component reaction–diffusion equation: $$ \partial_t u(x,t) = D \partial^2_x u(x,t) + R\left(u(x,t)\right)$$ Looking at systems that exhibit a peak solution (solitary localized ...
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232 views

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 $\varphi^4$ ...