Abstract
In this article, the lump-type solutions of the new integrable time-dependent coefficient (2+1)-dimensional Kadomtsev-Petviashvili equation are investigated by applying the Hirota bilinear technique and a suitable ansatz. The equation is applied in the modelling of propagation of small-amplitude surface waves in large channels or straits of slowly varying width, depth and non-vanishing vorticity. Applying the Bell’s polynomials approach, we successfully acquire the bilinear form of the equation. We firstly find a general form of quadratic function solution of the bilinear form and then expand it as the sums of squares of linear functions satisfying some conditions. Most importantly, we acquire two lump-type and a bell-shaped soliton solutions of the equation. To our knowledge, the lump type solutions of the equation are reported for the first time in this paper. The physical interpretation of the results are discussed and represented graphically.
Highlights
Nonlinear equations (NLEs) have been the subject of concentrate in different parts of numerical physical sciences, for example, material science, science, and so forth
The explanatory arrangements of such conditions are of essential significance since a great deal of scientific physical models are depicted by NLEs [1]
Lump solution is a kind of special rational function solutions localized along all directions in the space
Summary
Nonlinear equations (NLEs) have been the subject of concentrate in different parts of numerical physical sciences, for example, material science, science, and so forth. Lump solutions are important models to used to describe certain complicated physical phenomena in science [3]. The be integrable time-dependent coefficient (2+1)-dimensional Kadomtsev-Petviashvili model that will be studied in this work is given by Wazwaz [7]:. Lump Solitons to TDC KP Equation where ψ(x, t, y) is a function of the temporal variable t and two scaled spatial variables x and y. The lump soliton solutions to (1) have not been studied using the Hirota Bilinear methods. By applying the concept of Bell polynomials [3, 4] and Hirota Bilinear approach [12,13,14], the lump soliton solutions of (1) will be derived. A Bell-shaped soliton solution will be derived using an efficient ansatz [15]
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