Abstract
In this work, we present a new two-mode version to the complex Hirota equation. This new model arises in many applications in the field of optics, communications and other engineering sciences. It describes the propagation of two-symmetric solitary waves moving simultaneously with dependent phase-velocity parameter. The extended tanh-coth expansion method and the polynomial-function method are used to extract novel new cusp-type solutions to the Hirota model. A comprehensive graphical analysis is conducted to show physical aspects of this new type of nonlinear equations. The findings of this work are from mathematical point of view and we propose some benefits regarding the concept of two-mode where it could be visualized and practically applied.
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