# Bäcklund transformation, Pfaffian, Wronskian and Grammian solutions to the (3+1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(3+1)$$\end{document}-dimensional generalized Kadomtsev–Petviashvili equation

Bäcklund transformation, Pfaffian, Wronskian and Grammian solutions to the... With the Hirota bilinear method and symbolic computation, we investigate the (3+1)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$(3+1)$$\end{document}-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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Analysis and Mathematical Physics Springer Journals

# Bäcklund transformation, Pfaffian, Wronskian and Grammian solutions to the (3+1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(3+1)$$\end{document}-dimensional generalized Kadomtsev–Petviashvili equation

, Volume 11 (1) – Nov 22, 2020
24 pages

/lp/springer-journals/b-cklund-transformation-pfaffian-wronskian-and-grammian-solutions-to-x3JuwZQdZZ
Publisher
Springer Journals
ISSN
1664-2368
eISSN
1664-235X
DOI
10.1007/s13324-020-00414-y
Publisher site
See Article on Publisher Site

### Abstract

With the Hirota bilinear method and symbolic computation, we investigate the (3+1)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$(3+1)$$\end{document}-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.

### Journal

Analysis and Mathematical PhysicsSpringer Journals

Published: Nov 22, 2020