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In this work, we consider a (2 + 1)-dimensional asymmetric Nizhnik-Novikov-Veselov (ANNV) equation, which has applications in processes of interaction of exponentially localized structures. Based on the bilinear formalism and with the aid of symbolic computation, we determine multi-solitons, breather solutions, lump soliton, lump-kink waves and multi lumps using various ansatze's function. We notice that multi-lumps in the form of breathers visualize as a straight line. To realize dynamics, we commit diverse graphical analysis on the presented solutions. Obtained solutions are reliable in the mathematical physics and engineering.

This article is devoted to determine interactions of lump and various solitary wave solutions of the generalized (3+1)-D B-type Kadomtsev-Petviashvili (BKP) model which is frequently arises in fluid dynamics, plasma physics, and feebly dispersive media. Bearing in mind on the bilinear formalism and symbolic software Maple-18, we determine three types of interaction solutions of the model. The first type of interaction occurs between a lump wave and a stripe soliton exhibits elastic collisions. Second type of collision between exponential and trigonometric functions generates periodic lump type breather wave solutions. Besides this, the breather wave degenerate into a single lump wave is determined by using parametric limit scheme. Thirdly, we reflect a new interaction solution among lump, kink and periodic waves via 'rational-cosh-cos' type test function. Four different conditions on the exits parameters are illustrated with fission properties in the third case. In addition, we display the dynamical characteristics of the interaction solutions to reveal the evolutions and flow directions via 3D and contour profiles of the model.