Multi-soliton solutions for a (2+1)-dimensional variable-coefficient nonlinear Schrödinger equation

In this paper, a (2+1)-dimensional variable-coefficient nonlinear Schrödinger equation is investigated, which can describe an inhomogeneous Heisenberg ferromagnetic spin chain with the octupole-dipole interaction or alpha helical protein with higher-order excitations and interactions under the continuum approximation. Bilinear forms, one- and two-soliton solutions are derived by virtue of the Hirota method and symbolic computation. Propagation and interaction properties of the solitons are discussed: Parabolic, cubic and periodic solitons are presented. Amplitudes of the solitons are only related to the wave numbers, while the velocities are related to both the wave numbers and variable coefficients. Interactions between the two parallel solitons are discussed.