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This research explores similarity solutions of the nonlinear Schrodinger equation, suggesting new wave models in physics.
General similarity solution of the nonlinear Schrodinger equation is obtained by using group-theoretic methods. Similarity solutions for several special cases are also found. Finally, a solitary wave solution of the (1 + 2)-dimensional nonlinear Schrodinger equation in deep water is derived.
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A 1994 study studied this question.
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