Studying Lump solutions, Rogue wave solutions and dynamical interaction for new model generating from lax pair

M. K. Elboree¹

¹ Mathematics Department, Faculty of Science, South Valley University, Qena, Egypt.

Mathematical modelling of natural phenomena, Tome 15 (2020), article no. 67.

Résumé

In this paper, we consider the (3 + 1)-dimensional Burgers-like equation which arises in fluid mechanics, which constructed from Lax pair generating technique. The bilinear form for this model is obtained to construct the multiple-kink solutions. Lump solution, rogue wave solutions are constructed via the obtained bilinear form for this model. The physical phenomena for these solution are analyzed by studying the influence of the parameters for these solutions. The phase shifts, propagation directions and amplitudes for these solutions are controlled via these parameters. The collisions between the lump wave and the stripe soliton, which is called lumpoff solution are completely non-elastic interaction. Finally, the figures of the solutions are shown to study the dynamical behavior for the lump, rogue wave and the properties of the interaction phenomena under various parameters for (3 + 1)-dimensional Burgers-like equation. These results can’t be found in the previous scientific papers.

Détail

DOI : 10.1051/mmnp/2020029

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