An energy principle for soliton solutions with higher nonlinearities

The two-dimensional stability of Langmuir solitons in investigated taking into account the dynamic ion response and electron nonlinearities. A variational principle for the growth rate is derived which allows one to determine growth rates and regions of instability by standard numerical procedures. The validity of previous methods using trial functions and the variation of action method, as well as the limitations of the corresponding results for the growth rates, neglecting the dynamic ion response, are critically examined.