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This paper aims to study the Gramian solutions and solitonic interactions of a (2 + 1)-dimensional Broer–Kaup–Kupershmidt (BKK) system, which models the nonlinear and dispersive long gravity waves traveling along two horizontal directions in the shallow water of uniform depth.

Pfaffian technique is used to construct the Gramian solutions of the (2 + 1)-dimensional BKK system. Asymptotic analysis is applied on the two-soliton solutions to study the interaction properties.

N-soliton solutions in the Gramian with a real function ζ(y) of the (2 + 1)-dimensional BKK system are constructed and proved, where N is a positive integer and y is the scaled space variable. Conditions of elastic and inelastic interactions between the two solitons are revealed asymptotically. For the three and four solitons, elastic, inelastic interactions and soliton resonances are discussed graphically. Effect of the wave numbers, initial phases and ζ(y) on the solitonic interactions is also studied.

Shallow water waves are studied for the applications in environmental engineering and hydraulic engineering. This paper studies the shallow water waves through the Gramian solutions of a (2 + 1)-dimensional BKK system and provides some phenomena that have not been studied.

The purpose of this paper is to provide an investigation on a new kind of photocatalytic material, namely, the porous ceramic foam loading titanium dioxide, which can make an effective photocatalytic degradation of the methyl orange (MO) solution in the wastewater.

The natural zeolite powder has been used as the primary raw material to produce a sort of lightweight porous ceramic foam by impregnating polymer foam in slurry and then sintering. With the sol-gel method, a kind of open-cell reticular porous ceramic foam loading TiO₂ film was obtained having a good photocatalytic action, and the resultant porous composite product presents the bulk density of 0.3~0.6 g/cm³ to be able to float on water.

The MO could tend to be completely degraded in the solution with a certain concentration by the TiO₂-loaded ceramic foam irradiated with ultraviolet light, and this composite foam was found to have high degradation efficiency for the MO solution in a wide range of pH.

This work presents a TiO₂-loaded ceramic foam that can effectively photo-catalyze to degrade the MO in water, and the degradation efficiency were examined under different conditions of the MO solution with various pH values.