Extended nonlinear waves in multidimensional dynamical lattices (Q2655819)

Multi-legged extended nonlinear structures are examined in 2D and 3D discrete media via the identification of appropriate solutions to \[ i\dot u_n= -\varepsilon(\Delta_2u)_n- |u_n|^2u_n, \] where \(u_n\) is a complex lattice field, \(n\) is a vectorial lattice index, \(\Delta_2\) is a standard discrete Laplacian, and \(\varepsilon\) is the intersite coupling. The stability of the basic building blocks of the solutions is explored too in an analytical form, and found to be stable. The stability of the full extended nonlinear structures is studied numerically, which yields instability thresholds for such structures, which are attained with the increase of the lattice coupling constant.