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The temporal evolution of intense Langmuir waves in an unmagnetized plasma of two spatial dimensions is studied numerically. When the inequality W≳ (kλe)2 is satisfied, the evolution quickly leads to a state of collapsing solitons. Here, W is the ratio of electric field energy density to the particle kinetic energy density, k is a typical Langmuir wavenumber, and λe is the electron Debye length.
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Nicholson et al. (1978) studied this question.
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