New unexpected variety of solitons arising from spatio-temporal dispersion (1+1)-dimensional Ito-equation

Abstract

In this work, new varieties of unexpected scenarios for the solitons arising from the spatio-temporal dispersion ([Formula: see text])-dimensional Ito-equation (STDIE) are considered as an extension of the KdV (mKdV) type to higher order and usually employed to predict the rolling behavior of ships in regular sea. Moreover, they can describe the interaction process of two internal long waves specially the height of the water’s free surface above a flat bottom where [Formula: see text] is an analytic function. We will introduce these new unexpected and impressive scenarios for the solitons that emerged from this model for the first time in the framework of three distinct schemas. The three schemas that are employed for this target are the Paul-Painleve approach method (PPAM), the extended direct algebraic method (EDAM) and ([Formula: see text]/G)-expansion method. Our obtained solitons are new compared with that achieved before by other authors who applied various schemas.