Invertible Mappings of Nonlinear PDEs to Linear PDEs through Admitted Conservation Laws

被引：1

作者：

Stephen Anco

George Bluman

Thomas Wolf

机构：

[1] Brock University,Department of Mathematics

[2] University of British Columbia,Department of Mathematics

来源：

Acta Applicandae Mathematicae | 2008年 / 101卷

关键词：

Conservation laws; Linearization; Symmetries; 35A30; 58J70; 35L65; 35A34; 22E65; 70H33;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

An algorithmic method using conservation law multipliers is introduced that yields necessary and sufficient conditions to find invertible mappings of a given nonlinear PDE to some linear PDE and to construct such a mapping when it exists. Previous methods yielded such conditions from admitted point or contact symmetries of the nonlinear PDE. Through examples, these two linearization approaches are contrasted.

引用

页码：21 / 38

页数：17

共 50 条

[31] Topological charges and conservation laws involving an arbitrary function of time for dynamical PDEs
Anco, Stephen C.
Recio, Elena
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2021, 477 (2245):
[32] Image Processing and ‘Noise Removal Algorithms’—The Pdes and Their Invariance Properties & Conservation Laws
B. Al Qurashi
A. H. Kara
H. Akca
Acta Applicandae Mathematicae, 2018, 153 : 163 - 169
[33] Accuracy of classical conservation laws for Hamiltonian PDEs under Runge–Kutta discretizations
Jialin Hong
Shanshan Jiang
Chun Li
Numerische Mathematik, 2009, 112 : 1 - 23
[34] Image Processing and 'Noise Removal Algorithms'-The Pdes and Their Invariance Properties & Conservation Laws
Al Qurashi, B.
Kara, A. H.
Akca, H.
ACTA APPLICANDAE MATHEMATICAE, 2018, 153 (01) : 163 - 169
[35] Fast Poisson-based Solvers for Linear and Nonlinear PDEs
Xu, Jinchao
PROCEEDINGS OF THE INTERNATIONAL CONGRESS OF MATHEMATICIANS, VOL IV: INVITED LECTURES, 2010, : 2886 - 2912
[36] The variational iteration method for solving linear and nonlinear systems of PDEs
Wazwaz, Abdul-Majid
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2007, 54 (7-8) : 895 - 902
[37] A unified transform method for solving linear and certain nonlinear PDEs
Fokas, AS
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1997, 453 (1962): : 1411 - 1443
[38] On linear monotone iteration and Schwarz methods for nonlinear elliptic PDEs
Lui S.H.
Numerische Mathematik, 2002, 93 (1) : 109 - 129
[39] On linear monotone iteration and Schwarz methods for nonlinear elliptic PDEs
Lui, SH
NUMERISCHE MATHEMATIK, 2002, 93 (01) : 109 - 129
[40] Chaotic dynamics of linear hyperbolic PDEs with nonlinear boundary conditions
Xiang, Qiaomin
Yin, Zongbin
Zhu, Pengxian
CHAOS SOLITONS & FRACTALS, 2020, 131

← 1 2 3 4 5 →