Darboux transformation and exact one-soliton solution of the Fokas-Lenells equation - Жасыбаева M. Б.; Есмаханова , К. (BULLETIN OF THE L.N. GUMILYOV EURASIAN NATIONAL UNIVERSITY. PHYSICS. ASTRONOMY SERIES, 2022)
In this article, we consider an equation describing the propagation of ultrashort nonlinear light pulses in optical fibers, the so-called Fokas-Lenells equation (FLE). FLE is one of the generalizations of the nonlinear Schrodinger equation (NSE) and is integrable using the inverse scattering method. Also allows soliton or soliton-like solutions. For all known evolutionary nonlinear equations for the search for soliton solutions, one has to develop his own methods that take into account the features of this equation. In this paper, we propose a Darboux transformation (DT) method for FLE. To find a one-soliton solution is constructed of the equation in question, a 1-fold DT is constructed. Also, using the results obtained, one can find the two-soliton and N-soliton solutions of FLE.