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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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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 $\Psi(x,t)$, $$i \frac{\partial \Psi}{... 0answers 82 views ### Nonlinear Saturated Schrodinger Equation in 1D- Physical Models I'm studying the Nonlinear 1d Schrodinger equation$$i\psi _t + \psi '' + |\psi |^{2p} \psi - \epsilon |\psi | ^{2q} \psi = 0\, , \quad t>0, x\in \mathbb{R}\, ,$$and specifically, its solitary ... 0answers 54 views ### Why do vortices scatter at right-angles I have been taking a course on non-perturbative physics and currently the teacher is away so I cannot ask him. In the lectures, he made the claim that a pair of vortices in the abelian-Higgs model ... 1answer 66 views ### Solitons and its infinite extension A soliton, for example the KdV equation solution, has the profile proportional to a hyperbolic secant squared {\text{sech}}^{2}(x-ct). And since it is hyperbolic it has an exponential dependence, so ... 2answers 2k views ### Explanation of the waves on the water planet in the movie Interstellar? We will ignore some of the more obvious issues with the movie and assume all other things are consistent to have fun with some of these questions. Simple [hopefully] Pre-questions: 1) If the water ... 0answers 91 views ### Categorization of electromagnetic solitons? I've seen over the years several mentions of electromagnetic solitons that appear in the high-intensity regime (where vacuum polarization becomes important). Some of these are coupled with plasmas, ... 0answers 153 views ### KdV equation and classical linear wave equation Like we know, the standard form of KdV equation is$$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 ...
The following image is taken from p. 85 in the textbook Topological Solitons by N. Manton and P.M. Sutcliffe: What I don't understand from the above statement: why $e(\mu)$ has minimum for ...