Bilinear forms and soliton solutions for a (2+1)-dimensional variable-coefficient nonlinear Schrodinger equation in an optical fiber

In this paper, under investigation is a (2 + 1)-dimensional variable-coefficient nonlinear Schrodinger equation, which is introduced to the study of an optical fiber, where t is the temporal variable, variable coefficients a(t) and b(t) are related to the group velocity dispersion, c(t) and d(t) represent the Kerr nonlinearity and linear term, respectively. Via the Hirota bilinear method, bilinear forms are obtained, and bright one-, two-, three- and N-soliton solutions as well as dark one- and two-soliton solutions are derived, where N is a positive integer. Velocities and amplitudes of the bright/dark one solitons are obtained via the characteristic-line equations. With the graphical analysis, we investigate the influence of the variable coefficients on the propagation and interaction of the solitons. It is found that d(t) can only affect the phase shifts of the solitons, while a(t), b(t) and c(t) determine the amplitudes and velocities of the bright/dark solitons.