科研之友
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摘要
Using the nonlinear Schrodinger (NLS) equation, which is used to describe the propagation of the solitons in many real physical systems like fiber and plasma, as a simple example, a direct perturbation method is established. Up to the adiabatic (zero order) approximation, any waves of the NLS equation decay in the same rate. Especially, different from the known claims in literature, the decay rate of the dark soliton in fiber is the same as that of the bright soliton. Starting from any one of the infinitely many adiabatic symmetries (or conservation laws) of the nonperturbative NLS equation, one can get the same adiabatic solutions. An adiabatic symmetry by multiplying a decay factor is just the first order modification. Higher order modifications can be obtained by solving linear equations.
