Special soliton structures in the (2+1)-dimensional nonlinear Schrödinger equation with radially variable diffraction and nonlinearity coefficients

Abstract

Applying Hirota's binary operator approach to the (2+1)-dimensional nonlinear Schrödinger equation with the radially variable diffraction and nonlinearity coefficients, we derive a variety of exact solutions to the equation. Based on the solitary wave solutions derived, we obtain some special soliton structures, such as the embedded, conical, circular, breathing, dromion, ring, and hyperbolic soliton excitations. For some specific choices of diffraction and nonlinearity coefficients, we discuss features of the (2+1)-dimensional multisolitonic solutions.