2025/01/14 by Bernatska, Julia
#37J35 #37J37 #37J38 #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.2501.07862
Quasi-periodic solutions to the sine-Gordon equation are expressed in terms of \wp1,2g-1-function, and reality conditions are completely specified. This new result leads to computation and graphical representation of non-linear wave solutions. A way of obtaining the finite-gap solutions by means of algebro-geometric integration is exposed in detail, as well as the construction of the sine-Gordon hierarchy on coadjoint orbits in the loop algebra of \mathfraksu(2).