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

Abstract

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 [Formula: see text] 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.

Rogue waves on an elliptic function background in complex modified Korteweg–de Vries equation

“…After implementing the nonlinearization of Lax pair procedure, we obtain the coefficients (a and d) with the presence of eigenvalues (λ 1 ) for both the periodic waves. By using the above constraints (( 21) and ( 22)), we can rewrite the polynomial Q(λ) in equation (20) in terms of these parameters as follows:…”

“…A number of mathematical methods have been used to construct RW solutions, breather solutions of various kinds and different solitary wave solutions in the nonlinear evolution equations. To name a few we cite Darboux transformation (DT) method, Bäcklund transformation, Hirota bilinear method and so on [14][15][16][17][18][19][20]. Among these, DT method has been widely used to construct RW solutions of nonlinear partial differential equations.…”