Localized solutions of (5+1)-dimensional evolution equations

In this research, the general linear evolution equations (EEs) in (5+1) dimensions are studied. All the mixed second-order derivatives are included in this aforementioned model. Using the Hirota bilinear operator and symbolic computation, the localized solutions–the abundant lump solutions are constructed. Particularly, it is found that only four groups of linear (5+1)-dimensional EEs are found that they have abundant lump solutions, and no interactions between the lump and other solutions are found via the positive definite quadratic functions. Finally, four examples corresponding to the above-mentioned cases are given to validate the obtained results, and the corresponding graphs are presented to show the dynamic behaviors of the abundant lump solutions of these given examples.

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