Abstract
We consider the generalized Fokas–Lenells equation which has been become especially popular in recent years for the description soliton solutions in the optical fiber. This equation is studied by us using the traveling wave reduction. We find two first integrals for the system of equations corresponding to the imaginary and real part of dependent variable. These first integrals are used to transform the system of equations to the first-order nonlinear differential equation which can be presented in quadrature. Therefore, the problem of finding the general solution for the generalized Fokas–Lenells equation has been reduced to the calculation of the integral. Some special cases of the equation are considered and general solutions expressed via the elliptic and exponential functions are constructed.
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