Volume 24, Issue 3, June 2017, Pages 379 - 392
Primary Branch Solutions of First Order Autonomous Scalar Partial Differential Equations via Lie Symmetry Approach
Authors
S. Y. Lou*
Ningbo Collabrative Innovation Center of Nonlinear Harzard System of Ocean and Atmosphere and Faculty of Science, Ningbo University, Ningbo, 315211, China, and Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, China
Ruo Xia Yao
School of Computer Science, Shaanxi Normal University, Xi’an, 710062, China
*Email: lousenyue@nbu.edu.cn
Corresponding Author
S. Y. Lou
Received 12 February 2017, Accepted 20 April 2017, Available Online 6 January 2021.
- DOI
- 10.1080/14029251.2017.1341700How to use a DOI?
- Keywords
- Primary branch solutions; symmetry approach; Arbitrary first order scalar PDE
- Abstract
A primary branch solution (PBS) is defined as a solution with m independent n − 1 dimensional arbitrary functions for an m order n dimensional partial differential equation (PDE). PBSs of arbitrary first order scalar PDEs can be determined by using Lie symmetry group approach companying with the introduction of auxiliary fields. Because of the intrusion of the arbitrary function, the PBSs have abundant and complicated structure. Usually, PBSs are implicit solutions. In some special cases, explicit solutions such as the instanton (rogue wave like) solutions may be obtained by suitably fixing the arbitrary function of the PBS.
- Copyright
- © 2017 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - S. Y. Lou AU - Ruo Xia Yao PY - 2021 DA - 2021/01/06 TI - Primary Branch Solutions of First Order Autonomous Scalar Partial Differential Equations via Lie Symmetry Approach JO - Journal of Nonlinear Mathematical Physics SP - 379 EP - 392 VL - 24 IS - 3 SN - 1776-0852 UR - https://doi.org/10.1080/14029251.2017.1341700 DO - 10.1080/14029251.2017.1341700 ID - Lou2021 ER -