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# Solitons - Science topic

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Questions related to Solitons

Hi,

I am thinking about

**Solitons modeling**and would like to know which*“out of the box”*software products are readily available and how they compare with developing*one’s own**Linux/Unix**based package e.g. in C/C++ or Java??*Replies from Experienced

**N Solitons**modeling researchers with**links**will be much appreciated!**Open Source**solutions are Always Preferred ones.

Best regards,

George Yury Matveev

I'm searching for new collaborations. I'm focused mostly on numerics on obtaining solitons bifurcating from band edges and localized modes. I'm specialized in shooting methods with more than one parameter, NR optimized for CUDA obtaining solutions, parametric curve step to obtain branches that cannot be described by a function. Optimization of split-step FFT dynamics with coupled Nonlinear partial differential equations, Ex: SHG was the harder one. I worked previously with V. Konotop, F. Abdullaev and B. Malomed. I was first author on all papers. They provided the equations and researched on obtaining solutions.

To get a soliton train pulses from a ring laser cavity host a Saturable Absorber , we need to make a balance between the dispersion of the cavity active and passive elements . What is the EDF length that have to use and SFM 28 for example ?

Thank you for your advises !

Regardes .

It is well confirmed that the nonlinear evolution equation is widely used as a leading mathematical equation for describing the physical significance of many physics branches. But it is a challenging task to solve them. Recently, many researchers have proposed various types of analytic methods to construct the soliton solutions. Unfortunately, most of these methods lead to equivalent solutions. In my opinion, the methods with the equivalent solutions of NLEEs are not helpful for further verification in the laboratory. That is why my discussion topic is "Which are the most appropriate analytic methods to construct the soliton solutions for nonlinear evolution equations?".

Hello scientific community,

In your point of view, is it possible to include the terms of variation of the geometry of a channel in the analytical expression of the Serre-Green-Naghdi soliton?

I am looking to understand what is soliton in qft, not in optical devices because it seemed to me that solitons look very different in optical field than in qft, but I am trying to understand what this means and I am very confused about topological solitons , the solitons are like taking L = 1 2 ∂µφ∂µφ - U (φ) and after use a metric like mikosky metric, after this I could use euler lagrange for the field of motion equation and this would give me a non-relativistic lagragian , and the problem is that I cant get the static solution because I don't know how to do it, are the solitons a static solution for some potential? , Maybe solitons should exist only in the 1d + 1d field which has local symmetry u (1) or are there solitons in 3d + 1d? ,what means solitons in BRST quantazation bacuase i fell that brst dosent have any relatiship with solitons.

Is it possible to reformulate general relativity in terms of elasticity theory assuming spacetime is some isotropic elastic continuum? This will also lead to concepts of spacetime strains, stresses and stretching forces, also expressed as tensors in elasticity theory. Curving of spacetime would have a meaning of displacement from undisturbed state. If this is the case, what would be an analog of Young Module E of space?

The question is related to the concept of Atomic Solitons and AString Spacetime Quanta composing spacetime like in image attached

All mountain ranges are distinctly wavy, with sequential peaks and valleys, which implies some kind of wavy process during their formations.

The question to geologists:

- what process forms those geological waves; why waves?

- what the conventional geological theory (orogeny?) tells about WAVY mountains;

- is there a specific wave pattern (like number of peaks) in mountain ranges?

In a book Soliton Nature (https://www.amazon.com/-/e/B082F3MQ4L), we published the hypothesis of 'solitonic geological wave packets'

and YouTube video

But, not being specialist in geology, unsure about validity of solitonic hypothesis.

Any help with references to solid researches would be appreciated.

How to distinguish between travelling wave solutions and solitary wave solutions of nonlinear dispersive equation like KdV-Burgers' equation? While analysing the wave propagation of solution figue, how actually one identifies it as soliton?

Thanks in advance

A soliton (such as, KdV soliton) has to satisfy an infinite number of conservation laws. What are the physical names and significances of such solitonic conserved properties? Please explain elaborately with examples, illustrations and references.

I would like to know if soliton pulses are still employed in existing fiber optic communication systems. If yes, then please mention some of the existing commercial systems that use soliton pulses.

Considering the special conditions that are required for propagation of soliton pulses, I think it would be quite difficult to maintain soliton pulses in a WDM system.

About zero dispersion fiber and pulse shaping.

why do we normalized propagation distance and time , pulse ,in nonlinear Schrodinger equation ?

what is advantage of dark solitons in comparison with bright solitons ?

Solitons is the common but we are changing the structures which are also based on the common photonic crystal. Is there possibility of same kind of soliton in all three structures.

Paper offers simple formula for spacetime quanta as solitonic kink-like function AString(x) which satisfy the equation AString'(x) = AString(2x+1) - AString(2x-1) and capable to represent direction x in space as a superposition of quanta x = … AString(x-2s) + AString(x-s) + AString(x) + AString(x+s) + AString(x+2s)… as shown in pictures. AString is an integral and compounding block of well-known finite Atomic Function up(x) introduced in 1971 by V.L. Rvachev.

The question to Spacetime Quantisation (STQ) specialists : is there other alternatives to represent a spacetime continuum via other kind of functions?

The light,optical pulse and solitons propagation in nonlinear medium? Specify the main physics concepts? What are the necessary conditions for propagation and to develop other effects .

Recently, we have derived a

**new equation**from Geophysical Fluid mechanics with the following presentation in the attached file.**We wonder about two facts:**

**(1) When is it integrable?**

**{2} Could we find the solutions for the equation? such as the solitons, N-solitons etc..?**

Have you ever encountered the equation, and I am looking forward to your help. Thank you for your suggestive references!

Their are number of solitons are possible in photonic crystals. Some of them are available in literature.

Non-Linear waves propagating in plasmas

Would you be interested in https://www.researchgate.net/publication/322520021_Introducing_Financial_Market_Solitons

which expands theory of solitons to new domains - similar to your project.

Is this meant as solitons? I think that I read that EM field does not have solitonslike solutions in most cases. But if they are solitons how is their ability accounted for to 'feel' entire space in almost 0 time (as is evident from Feynman trajectories approach)?

In a box the exitations imerge immediately and comprise the whole length of the box. So there is a probability to detect a photon far from the source. How is this to be consistent with the constancy of speed of light c?

Many nonlinear equations are solved for soliton solutions using Hirota bilinearization method but those equations are proven to be integrable either in inverse scattering sense or Lax pair method. Is it correct to use the Hirota bilinearization for nonintegrable systems?

Domain walls have different shape and functions in ferroics, so are they topological defects?

I am doing research on evanescent fields and I'm curious as to whether or not a decaying exponential field can have a complex shape if it passes through nanolithography scale structures. (Examples of papers that state this would be helpful) Perhaps someone with COMSOL (or a similar simulation software) could help me out?

From thinking about it I'm fairly certain it would, say if you had in a simple case an evanescent field generated at an interface where there was a nanolithographic step, you would probably get a transition at the step where the field would not have the same penetration depth as it does in either part of the step.

I know how it works but I want to know the fundamental reason which relates eigan value analysis to the stability analysis of a linear system. Everywhere I searched, I came across examples about how eigan values have been used but I want to understand how eigan values came to play such a big role in the field of stability analysis. How is it helpful in uncovering the "underlying structure" of a system, which is what it does actually ? Can someone point me towards some good literature that would enlighten me in that direction ?

Waves in nonlinear media with dissipation are called shock waves. The waves in nonlinear media with a dispersion are called solitons. But what are the name of waves in nonlinear media with dispersion and dissipation? And how this type of waves can be doubtlessly identified in the experiment?

In the coefficients of Mie scattering Riccati- Bessel function appears. What is the significance of these functions in the context of Mie -scattering?

It is well known that certain integrable equations such as the Camassa-Holm, Novikov and Qiao admit the so-called peakon solutions. However, all of them are not evolution equations. Then I would like to know if there is some evolution equation admitting such property.

Is there an initial condition for collison of solitons as Gaussian initial condition and undular bore initial condition? Could somebody help me, please?

Individual photons travel in "empty" space for very long distances maintaining (except for red shift and other subtle effects) their wavelength, energy, momentum, and do not disperse or diffuse.

If a pair of photons have paths that cross each other and they coincide in time (empty space understood) apparently they interact and then leave the interaction to run their errands further down their previous trajectories. The idea of a photon being some sort of classical three dimensional electromagnetic soliton is therefore a natural one. But Maxwell equations do not seem to handle these properties.

Is a good, consistent, understandable treatment of photons as electromagnetic solitons known to someone?

Cordially,

Daniel

I have generated explicit soltion solutions for coupled nonlocal nonlinear schrodinger equation. Now, want to check the stability of the solution by NUMERICAL ANALYSIS. I am not familiar with any methods can anyone suggest me to do it.

Thanks in advance.

Good morning, I am a graduate student, new in researching the transmission and stability of optical solitons. I've read some articles about it, and a method named

*'Vakhitov–Kolokolov criterion'*have been metioned many times. I am curious about it, also confused.**Could anyone tell me about**

*Vakhitov–Kolokolov criterion*in briefly, or introduce some articals deducing it detailedly to me?I will be deeply grateful.

This is less a question, more a request for confirmation of my understanding of some reading I've done. Is the following true?

For asymptotically flat solitons (generalisations of Bartnik and McKinnon's su(2) solutions), it appears that the asymptotic values of the gauge fields (i.e. for r tending to infinity) are fixed to certain integer values, which means that the tangential pressure P vanishes at infinity. This in turn means the solutions carry

**no**global magnetic charge, for if they did, the Einstein equations would be singular at infinity.If anyone could either confirm this, or else point out my error(s), I'd much appreciate it.

If I just put up a thulium fiber laser system which is working in the analmalous region, however, I just want to use some optical devices to change the whole dispersion in the cavity from negative dispersion into positive dispersion. Has anyone known this?

Skyrmions, Magnetic Solitons - Domain walls are considered topological defects

If we consider a two component BEC, in such regime, the solitonic solutions leads to the formation of a bound state. This bound state formation occurs only when one component follows dark soliton and other one is bright soliton. My question is what is the importance of such bound state in the literature? By importance, I mean to say what are the applications of such bound states in BEC?

Thanks in advance for your kind comments.

I mean acoustic or lattice solitary wave.

I'm trying to simulate the pulse propagation in HC-PCF using the professor Govind Agrawal's NLSE solver software [attached]. I think this software can't fulfill all the HC-PCF parameters requirements. Thats why I'm not getting the desired output even i'm using the same parameter values from the papers (attached).

Can anyone please help me in this regard ?

It is known that Self-Dual Yang Mills theory reduces to Korteweg-deVries equation or its modified form (mKdV), see the file included. Then it seems possible to consider hadrons as solitons. For a review of various models, see Stephan Hartmann's paper: http://core.kmi.open.ac.uk/download/pdf/11921144.pdf

But as far as I know, there is no convincing theory which is able to describe soliton model of quark masses. Or does anybody know a recent progress in this soliton approach of hadrons? Your comments are welcome.

Using the Grammian Determinant one can write N-soliton solution for the Complex Field equations like NLS equation. But is it possible to write N-soliton solution in the case of real field integrable equations (KdV,mKdV,extended KdV equations)?

As I know, all of the studies have explored the spatial profile of light passing through a nonlinear nanosuspension via solution of spatial part of Nonlinear Schrodinger Equation (NLSE) or wave equation. (For example they have derived soliton stripes) However, no other paper can be found to describe time evolution of light inside such nonlinear medium. Why?

Solitons are the 1D topological defect with phase singularity of \pi, whereas vortices have \2pi phase jump around its core. Recently the obsevation of solitonic vortex in BEC has been confirmed. Can anybody elaborate solitonic vortex clearly?

I understand this is common in femtosecond fiber lasers. This is because of instability in the soliton formed due to the long nonlinear interaction lengths in fibers. But what if I observe similar sideband from the Ti:Sapphire laser oscillator. Is this detrimental to the laser performance ?

I have seen that in different problems, different types of transformation are used. Why can't we use the same form for all problems? What does it actually mean?

Does anyone know how to simulate soliton propagation in a ring? How to adjust the dispersive and nonlinearity coefficients? Shall it be solved in 2D or 3D?

The system of equations

u_t + (\partial_x^2 + \partial_y^2)u_x + u u_x/2 = -(p_x u_x + p_y u_y)/2 (Eq. 1)

p_xx + p_yy = u_x (Eq. 2)

reduces to the KdV equation if u and p are independent of y. The KdV equation can of course be solved using the inverse scattering transformation (IST). Can the system of equations (1) and (2) be solved by the IST when u and p depend on x, y and t? [These equations arise in the theory of electromigration in thin films --- see R. M. Bradley, Physica D 158, 216 (2001)].

In optics, the term soliton is used to refer to any optical field that does not change during propagation because of a delicate balance between nonlinear and linear effects in the medium. Can they be considered as a viable optical energy carrier without attenuation issues?