New similarity solutions for the modified Boussinesq equation

In this paper the author presents some new similarity solutions of the modified Boussinesq equation, which is a completely integrable soliton equation. These new similarity solutions include reductions to the second and fourth Painleve equations which are not obtainable using the standard Lie group method for finding group-invariant solutions of partial differential equations; they are determined using a new and direct method which involves no group theoretical techniques.

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