Abstract
In this paper, we aim to introduce a new form of the (3+1)-dimensional generalized Kadomtsev-Petviashvili equation for the long waves of small amplitude with slow dependence on the transverse coordinate. By using the Hirota’s bilinear form and the extended homoclinic test approach, new exact periodic solitary-wave solutions for the new (3+1)-dimensional generalized Kadomtsev-Petviashvili equation are presented. Moreover, the properties and characteristics for these new exact periodic solitary-wave solutions are discussed with some figures.
Highlights
Many nonlinear phenomena appear in marine engineering, fluid dynamics, plasma physics, chemistry, physics and so on
It is well known that nonlinear evolution equations are significantly important in describing nonlinear phenomena
The completely integrable KP equation describes the evolution of quasi-one-dimensional shallow-water waves when effects of the surface tension and the viscosity are negligible.[50]
Summary
Many nonlinear phenomena appear in marine engineering, fluid dynamics, plasma physics, chemistry, physics and so on. It is well known that nonlinear evolution equations are significantly important in describing nonlinear phenomena The research on these nonlinear evolution equations has increased important to get an insight through qualitative and quantitative features of these equations. A generalized (3+1)-dimensional KP equation was presented and discussed.[51–53] Multiple-soliton solutions, Wronskian and Grammian formulations were obtained for this generalized (3+1)-dimensional KP equation
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