Abstract
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.
Highlights
Lax pair generating technique is a vigorous tool to construct integrable equations in (2+1) dimensions [3]
The (3 + 1)-dimensional Burgers-like equation has a class of the positive quadratic function, the lump solutions can be expressed in the form f (x, y, z, t) = g2 + h2 + a6, g = a1x + a2y + a3z + a4t + a5, h = b1x + b2y + b3z + b4t + b5
We investigated lump solitons and rogue wave solutions for this equation via the bilinear method, these solutions are non-singular and localized and shown by density and 3D plots for a special parameters solution by Maple
Summary
Lax pair generating technique is a vigorous tool to construct integrable equations in (2+1) dimensions [3]. Keywords and phrases: Bilinear formalism, lump solitons, rogue wave solutions, (3 + 1)-dimensional Burgers-like equation, lump-stripe soliton interaction.
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