Abstract
Based on the bilinear method, rational lump and mixed lump-solitary wave solutions to an extended (2+1)-dimensional KdV equation are constructed through the different assumptions of the auxiliary function in the trilinear form. It is found that the rational lump decays algebraically in all directions in the space plane and its amplitude possesses one maximum and two minima. One kind of the mixed solution describes the interaction between one lump and one line solitary wave, which exhibits fission and fusion phenomena under the different parameters. The other kind of the mixed solution shows one lump interacting with two paralleled line solitary waves, in which the evolution of the lump gives rise to a two-dimensional rogue wave. This shows that these three interesting phenomena exist in the corresponding physical model.
Highlights
The study of integrable nonlinear systems has become a hot topic in wave propagations and mathematical physics
A lot of rational lump solutions, hybrid solutions consisting of lump waves and kink waves, loop-like kink breather solutions, and the lump interacting with the line soliton solutions have been constructed via the Hirota bilinear method [19–46]
We find that the rational lump solution u in equation (10) possesses the maximum amplitude −ðð4βða1a6 − a2a5Þ2Þ/ðαða21 + a25Þða22 + a26ÞÞÞ, which is centered at the point a2a8
Summary
The study of integrable nonlinear systems has become a hot topic in wave propagations and mathematical physics. A lot of rational lump solutions, hybrid solutions consisting of lump waves and kink waves, loop-like kink breather solutions, and the lump interacting with the line soliton solutions have been constructed via the Hirota bilinear method [19–46] These results can be derived by Darboux transformation [47–50], modified extended mapping method [1], and direct algebraic method [2], the bilinear method is still a powerful tool for solving integrable systems. We aim to construct the rational lump and the lump-solitary wave solutions to the extended (2+1)-dimensional KdV equation (2) through the trilinear form.
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call