Lump, rogue wave, multi-waves and Homoclinic breather solutions for (2+1)-Modified Veronese Web equation

This work addresses the four main inducements: Lump, rogue wave, Homoclinic breather and multi-wave solutions for (2+1)-Modified Veronese Web (MVW) equation via Hirota bilinear approach and the ansatz technique. This model is a linearly degenerate integrable nonlinear partial differential equation (NLPDE) and can also be used to admit a differential covering with nonremoval physical parameters. By assuming the function f in the Hirota bilinear form of the presented model as the general quadratic function, trigonometric function and exponential function form, also with appropriate set of parameters, we have prevented the lump, rogue wave, breather and multi-wave solutions successfully. A precise compatible wave transformation is utilized to obtain multi-wave solutions of governing model. Also, the motion track of the lump, Rogue wave and multi-waves is also explained both physically and theoretically. These new results contain some special arbitrary constants that can be useful to spell out diversity in qualitative features of wave phenomena.

Automated summary

This study addresses four main inducements (lump, rogue wave, Homoclinic breather, and multi-wave solutions) for the (2+1)-Modified Veronese Web (MVW) equation using Hirota bilinear approach and ansatz technique. By assuming different forms of the function f in the Hirota bilinear form, the study successfully prevented lump, rogue wave, breather, and multi-wave solutions. A precise compatible wave transformation was utilized to obtain multi-wave solutions, and the motion tracks of lump, rogue wave, and multi-waves were explained both physically and theoretically, providing new insights into the qualitative features of wave phenomena.