5 citations · 6 across the 4 of their papers we have counts for
4 papers
Multiscale limit for finite-gap Sine-Gordon Solutions and Calculation of Topological Charge using Theta-functional Formulae
P. G. Grinevich, K. V. Kaipa
In this paper, we introduce the so-called multiscale limit for spectral curves, associated with real finite-gap Sine-Gordon solutions. This technique allows to solve the old proble…
Calculation of Topological Charge of Real Finite-Gap sine-Gordon solutions using Theta-functional formulae
P. G. Grinevich, K. V. Kaipa
The most basic characteristic of x-quasiperiodic solutions u(x,t) of the sine-Gordon equation u_{tt}-u_{xx}+\sin u=0 is the topological charge density denoted . The real fi…
Spectral conservation laws for periodic nonlinear equations of the Melnikov type
P. G. Grinevich, I. A. Taimanov
We consider the nonlinear equations obtained from soliton equations by adding self-consistent sources. We demonstrate by using as an example the Kadomtsev-Petviashvili equation tha…
Infinitesimal Darboux transformations of the spectral curves of tori in the four-space
P. G. Grinevich, I. A. Taimanov
We study the action of conformal transformations of the ambient space on the Dirac operator coming into the Weierstrass (or spinor) representation of a torus in the Euclidean four-…