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Similarity solutions of the one and two-dimensional nonlinear Schrödinger equations are studied by means of Lie's method of infinitesimal transformation groups. It is shown that the two-dimensional nonlinear Schrödinger equation can be reduced to the nonlinear Klein-Gordon equation and others, and the solution of the one-dimensional nonlinear Schrödinger equation for a similarity variable is reducible to the second Painlevé transcendent. Some similarity solutions of the equations are obtained.
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Masayoshi Tajiri (1983) studied this question.
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