Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [soliton-theory]

The soliton-theory tag is for any questions regarding exactly solvable nonlinear PDE's such as Korteweg-De Vries, nonlinear Schrödinger, Sine-Gordon, etc. Other important related concepts are the Lax Pair, the AKNS Scheme, the Inverse Scattering Transform, the Gel'fand-Levitan-Marchenko equation, and the scattering data.

The tag is for any questions regarding exactly solvable nonlinear PDE's such as Korteweg-De Vries, nonlinear Schrödinger, Sine-Gordon, etc. Other important related concepts are the Lax Pair, the AKNS Scheme, the Inverse Scattering Transform, the Gel'fand-Levitan-Marchenko equation, and the scattering data.

See the Inverse Scattering Transform wiki for more information and references.

41 questions
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Is it possible to get the fourier transformation of complex sech function?

When I deal with soliton problem in optics, I get a complex amplitude function in the time domain as $$E(t)=\text{sech}\left(\frac{t}{a}\right)\text{exp}[i(bt^2+c)]$$ where $a$, $b$ and $c$ are non-zero constant. The problem is how to analytically…
Chao Mei
  • 21
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Solving the equation of a kink

Good morning. I was trying to calculate soliton-type solutions (kinks) in Rajarman's book, particularly with a potential of the form $$ U(\phi) = \frac{1}{2} \phi^2(\phi^2-1)^2 $$ According to the book, to obtain this solution, one must solve the…
Gorga
  • 47
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1 answer

What is an on-site (off-site) soliton?

Could you explain to me what a on-site resp. off-site soliton is? And maybe what is a localized mode and internal mode of a soliton? I cannot find explanations for these notions. Thank you in advance.
Rhjg
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0
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1 answer

On Manton's "mechanical" argument in monopole theory

In Chap. 1 of Atiyah and Hitchin's book "The Geometry and Dynamics of Magnetic Monopoles", the authors mention a "mechanical" argument due to N. Manton. Let $\mathcal{A}$ be the space of all pairs $(A,\phi)$, where $A$ is a connection on a principal…
Malkoun
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