Applied Mathematics & Information Sciences

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A direct rational exponential scheme is proposed to construct exact multi-soliton nonlinear partial differential equations. As an example we consider the well-known nonlinear Hirota-Ramani equation to investigate one-soliton, two-soliton and three-soliton solutions. This work is motivated by the fact that the direct rational exponential method provides completely non-elastic multi-soliton solution although soliton should remain their shape and size unchanged after and before collision. Furthermore, the properties of the acquired multiple soliton solutions are shown by three-dimensional profiles. All solutions are stable and might have applications in physics.

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