SOLITON SOLUTIONS FOR THE (2+1)-DIMENSIONAL INTEGRABLE FOKAS-LENELLS EQUATION

Аннотация

Studying of solitons led to the discovery of a number of new directions related to it. There is interest in
which is also enhanced in connection with the discovery of new examples in which soliton processes are manifested.
The number and variety of nonlinear equations containing solitons as the most interesting solutions significantly
increase due to generalizations to the two-dimensional and three-dimensional cases. Such popular transformations as
Darboux, Backlund and Hirota's bilinear method are often used to find exact different kind of the solutions of
nonlinear equations.
In the present paper, we present Lax pair of the (2+1)-dimensional integrable Fokas-Lenells equation. The
bilinear form of the (2+1)-dimensional integrable Fokas-Lenells equation was obtained by the Hirota’s bilinear
method. By using Hirota's bilinear method, we construct exact one-soliton and two-soliton solutions of the (2+1)-
dimensional Fokas-Lenells equation. The graphics of the obtained solutions are presented. The obtained new results
have important physical applications.