Abstract
In fluid mechanics, the higher-dimensional and higher-order equations are constructed to describe the propagations of nonlinear waves. In this paper, we investigate the (2+1)-dimensional variable-coefficient Caudrey-Dodd-Gibbon-Kotera-Sawada equation in fluid mechanics. The Nth-order Pfaffian solutions are constructed and proved via the modified Pfaffian technique. The higher-order soliton, first- and second-order breather solutions are constructed based on the Nth-order Pfaffian solutions. We graphically demonstrate that the amplitudes and velocities of the solitons are affected by some variable coefficients. Hybrid solutions composed of breathers, lumps and solitons are illustrated graphically. It can be found that when certain parameters are chosen, the breathers, lumps and solitons included in the hybrid solutions possess the same properties as those of the breather and lump solutions.
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