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Serguei Brazovskii and Natasha Kirova Natal 2012 Physics of synthetic conductors as low dimensional correlated electronic systems. Lecture 5, part 1. Solitons, the theory , l ast comments. E. 2k F. π/2a. 2k F. -π/2a. Ansatz : any term has the same structure. - The KdV eq.
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SergueiBrazovskii and Natasha Kirova Natal 2012 Physics of synthetic conductors as low dimensional correlated electronic systems. Lecture 5, part 1 Solitons, the theory, last comments
E 2kF π/2a 2kF -π/2a
Ansatz: any term has the same structure - The KdV eq.
- (xU)2= U3 -C1U-C2=(U-E+)(U-E_)(U-Ebot) Single wave E+=Ebot=E0 Taking x as a time, we get a motion of a particle in the cubic single-wall potential. Array of humps given by the Weierstrass or Jacobi elliptic function Ebot E- E+ Parameters of the elliptic function regulates the array periodicity with shapes evolving from isolated humps to a simple sinusoid = CDW.