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Transverse instability of soliton solutions to nonlinear Schrödinger equations

An inverstigation is made of the transverse instability of plane soliton solutions of the nonlinear Schrödinger equation, including the case of an exponential nonlinearity. The analysis is based on a variational method, where specific trial functions are applied for the perturbations. Explicit expressions for the growth rates are given, showing good agreement with numerical results.