Application of the Hirota method for the higher-order nonlinear Schrӧdinger equations

The Hirota method is applied to look for the soliton solutions of nonlinear higher order Schrӧdinger equations. The equations of the fourth and sixth orders of the Schrodinger hierarchy are studied in detail. Using the formulas for derivatives of the functions for the higher order equations are represented via the Hirota operator. The equations are presented as a system of two equations. One, two and three soliton solutions of the nonlinear Schrӧdinger hierarchy are obtained.

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