Stability of solitons described by nonlinear Schrِdinger-type equations with higher-order dispersion

Steady solitons described by the fourth order nonlinear Schrِdinger type equations in one, two and three dimensions with power-law nonlinearities are studied. Conditions of existence and stability of such solitons are found. Numerical results demonstrating soliton existence, stability and instability are described. They agree with the developed theory.