Nondegenerate solitons of the(2+1)-dimensional coupled nonlinear Schr?dinger equations with variable coefficients in nonlinear optical fibers

We derive the multi-hump nondegenerate solitons for the(2 + 1)-dimensional coupled nonlinear Schr?dinger equations with propagation distance dependent diffraction, nonlinearity and gain(loss) using the developing Hirota bilinear method, and analyze the dynamical behaviors of these nondegenerate solitons. The results show that the shapes of the nondegenerate solitons are controllable by selecting different wave numbers, varying diffraction and nonlinearity parameters.In addition, when all the variable coefficients are chosen to be constant, the solutions obtained in this study reduce to the shape-preserving nondegenerate solitons. Finally, it is found that the nondegenerate two-soliton solutions can be bounded to form a double-hump two-soliton molecule after making the velocity of one double-hump soliton resonate with that of the other one.