Physics

Pure mathematics

Bilinear interpolation

Pfaffian

Mathematics

Wronskian

Biology

Partial differential equation

Gene

Statistics

Mathematical analysis

Paleontology

Eigenvalues and eigenvectors

Kadomtsev–Petviashvili equation

Chemistry

Transformation (genetics)

Context (archaeology)

Characteristic equation

Quantum mechanics

Applied mathematics

Biochemistry

Gramian matrix

Bilinear form

Analysis and Mathematical Physics

With the Hirota bilinear method and symbolic computation, we investigate the $$(3+1)$$ ( 3 + 1 ) -dimensional generalized Kadomtsev–Petviashvili equation. Based on its bilinear form, the bilinear Bäcklund transformation is constructed, which consists of four equations and five free parameters. The Pfaffian, Wronskian and Grammian form solutions are derived by using the properties of determinant. As an example, the one-, two- and three-soliton solutions are constructed in the context of the Pfaffian, Wronskian and Grammian forms. Moreover, the triangle function solutions are given based on the Pfaffian form solution. A few particular solutions are plotted by choosing the appropriate parameters.

Bäcklund transformation, Pfaffian, Wronskian and Grammian solutions to the $$(3+1)$$-dimensional generalized Kadomtsev–Petviashvili equation