Exact solution and exotic coherent soliton structures of the (2+1)-dimensional generalized nonlinear Schrödinger equation

In this paper, a variable separation approach is used to obtain localized coherent structures of the (2+1)-dimensional generalized nonlinear Schrodinger equation:\rm i\varphi_t-(\alpha \beta)\varphi_xx+(\alpha+\beta)\varphi_yy-2\lambda \varphi \bigg(\alpha+\beta)\bigg(\int_-\infty^x|\varphi|_y^2\rm d x+u_1(y,t)\bigg) -(\alpha-\beta)\bigg(\int_-\infty^y|\varphi|_x^2\rm dy+u_2(x,t)\bigg)\bigg=0. By applying a special B?cklund transformation and introducing arbitrary functions of the seed solutions, the abundance of the localized structures of this model are derived. By selecting the arbitrary functions appropriately, some special types of localized excitations such as dromions, dromion lattice, breathers and instantons are constructed.