Paul-Painlevé analysis, soliton and periodic wave in the fractional thermophoretic motion equation via graphene sheets. (English) Zbl 1537.35148
Summary: We focused on solitonic phenomena in substrate-supported graphene sheets by learning the solitons of fractional thermophoretic motion equation, which was extracted from wrinkle wave motions. By utilizing the analytical technique and selecting suitably the improved \(\tan(\phi/2)\)-expansion method involved in the nonlinear ODE form, the new exact solutions are attained. Soliton, bright-dark soliton and periodic are studied with usage of symbolic computation. In addition, more symbolic computation by transformed to ODE for governing model is considered. Through three-dimensional graph, density graph, and two-dimensional design using Maple, the physical features of single soliton and periodic wave solutions are explained all right. The findings demonstrate the investigated model’s broad variety of explicit solutions. As a result, the exact solitary wave solutions to the studied issues, including solitary, single soliton, and periodic wave solution are found. It is shown that the Paul-Painlevé approach is practical and flexible in mathematical physics. All outcomes in this work are necessary to understand the physical meaning and behavior of the explored results and shed light on the significance of the investigation of several nonlinear wave phenomena in sciences and engineering.
MSC:
| 35C08 | Soliton solutions |
| 35Q51 | Soliton equations |
| 35R11 | Fractional partial differential equations |
Keywords:
fractional thermophoretic motion equation; periodic type; bright-dark soliton solutions; Paul-Painlevé operator; travelling waveReferences:
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