A new method to obtain approximate symmetry of nonlinear evolution equation from perturbations

doi:10.1088/1674-1056/18/7/002

中国物理B ›› 2009, Vol. 18 ›› Issue (7): 2629-2633.doi: 10.1088/1674-1056/18/7/002

A new method to obtain approximate symmetry of nonlinear evolution equation from perturbations

雍雪林¹, 张智勇², 陈玉福²

(1)Department of Mathematics and Physics, North China Electric Power University, Beijing 102206, China; (2)School of Mathematical Sciences, Graduate University of Chinese Academy of Sciences, Beijing 100049, China

收稿日期:2008-10-09 修回日期:2008-11-17 出版日期:2009-07-20 发布日期:2009-07-20

A new method to obtain approximate symmetry of nonlinear evolution equation from perturbations

Zhang Zhi-Yong(张智勇)^a)†, Yong Xue-Lin(雍雪林)^b), and Chen Yu-Fu(陈玉福)^a)

^a School of Mathematical Sciences, Graduate University of Chinese Academy of Sciences, Beijing 100049, China; ^b Department of Mathematics and Physics, North China Electric Power University, Beijing 102206, China

Received:2008-10-09 Revised:2008-11-17 Online:2009-07-20 Published:2009-07-20

摘要/Abstract

摘要： A novel method for obtaining the approximate symmetry of a partial differential equation with a small parameter is introduced. By expanding the independent variable and the dependent variable in the small parameter series, we obtain more affluent approximate symmetries. The method is applied to two perturbed nonlinear partial differential equations and new approximate solutions are derived.

Abstract: A novel method for obtaining the approximate symmetry of a partial differential equation with a small parameter is introduced. By expanding the independent variable and the dependent variable in the small parameter series, we obtain more affluent approximate symmetries. The method is applied to two perturbed nonlinear partial differential equations and new approximate solutions are derived.

Key words: approximate symmetry, approximate solutions, expansion, perturbed equation

中图分类号: (Partial differential equations)

02.30.Jr

02.20.Qs (General properties, structure, and representation of Lie groups)

张智勇, 雍雪林, 陈玉福. A new method to obtain approximate symmetry of nonlinear evolution equation from perturbations[J]. 中国物理B, 2009, 18(7): 2629-2633.

Zhang Zhi-Yong(张智勇), Yong Xue-Lin(雍雪林), and Chen Yu-Fu(陈玉福). A new method to obtain approximate symmetry of nonlinear evolution equation from perturbations[J]. Chin. Phys. B, 2009, 18(7): 2629-2633.

[1]	Ming-Jing Du(杜明婧), Bao-Jun Sun(孙宝军), and Ge Kai(凯歌). Adaptive multi-step piecewise interpolation reproducing kernel method for solving the nonlinear time-fractional partial differential equation arising from financial economics[J]. 中国物理B, 2023, 32(3): 30202-030202.
[2]	Yiyuan Zhang(张艺源), Ziqi Liu(刘子琪), Jiaxin Qi(齐家馨), and Hongli An(安红利). Soliton molecules, T-breather molecules and some interaction solutions in the (2+1)-dimensional generalized KDKK equation[J]. 中国物理B, 2023, 32(3): 30505-030505.
[3]	Jing Yue(岳靖), Jian Li(李剑), Wen Zhang(张文), and Zhangxin Chen(陈掌星). The coupled deep neural networks for coupling of the Stokes and Darcy-Forchheimer problems[J]. 中国物理B, 2023, 32(1): 10201-010201.
[4]	Liang'an Huo(霍良安) and Xiaomin Chen(陈晓敏). Dynamical behavior and optimal impulse control analysis of a stochastic rumor spreading model[J]. 中国物理B, 2022, 31(11): 110204-110204.
[5]	Jing Wang(王静), Xue-Li Ding(丁学利), and Biao Li(李彪). Fusionable and fissionable waves of (2+1)-dimensional shallow water wave equation[J]. 中国物理B, 2022, 31(10): 100502-100502.
[6]	Xiao-Qian Yang(杨晓倩), En-Gui Fan(范恩贵), and Ning Zhang(张宁). Propagation and modulational instability of Rossby waves in stratified fluids[J]. 中国物理B, 2022, 31(7): 70202-070202.
[7]	Xi-zhong Liu(刘希忠) and Jun Yu(俞军). A nonlocal Boussinesq equation: Multiple-soliton solutions and symmetry analysis[J]. 中国物理B, 2022, 31(5): 50201-050201.
[8]	Liang'an Huo(霍良安) and Yafang Dong(董雅芳). Dynamics and near-optimal control in a stochastic rumor propagation model incorporating media coverage and Lévy noise[J]. 中国物理B, 2022, 31(3): 30202-030202.
[9]	Yarong Xia(夏亚荣), Ruoxia Yao(姚若侠), and Xiangpeng Xin(辛祥鹏). Darboux transformation and soliton solutions of a nonlocal Hirota equation[J]. 中国物理B, 2022, 31(2): 20401-020401.
[10]	Liang'an Huo(霍良安) and Xiaomin Chen(陈晓敏). Near-optimal control of a stochastic rumor spreading model with Holling II functional response function and imprecise parameters[J]. 中国物理B, 2021, 30(12): 120205-120205.
[11]	Geng Zhang(张埂) and Da-Dong Tian(田大东). Stability analysis of multiple-lattice self-anticipative density integration effect based on lattice hydrodynamic model in V2V environment[J]. 中国物理B, 2021, 30(12): 120201-120201.
[12]	Ru-Qi Li(李汝琦), Yu-Rong Song(宋玉蓉), and Guo-Ping Jiang(蒋国平). Prediction of epidemics dynamics on networks with partial differential equations: A case study for COVID-19 in China[J]. 中国物理B, 2021, 30(12): 120202-120202.
[13]	Ying Yang(杨颖), Yu-Xiao Gao(高玉晓), and Hong-Wei Yang(杨红卫). Analysis of the rogue waves in the blood based on the high-order NLS equations with variable coefficients[J]. 中国物理B, 2021, 30(11): 110202-110202.
[14]	Ping Liu(刘萍), Bing Huang(黄兵), Bo Ren(任博), and Jian-Rong Yang(杨建荣). Consistent Riccati expansion solvability, symmetries, and analytic solutions of a forced variable-coefficient extended Korteveg-de Vries equation in fluid dynamics of internal solitary waves[J]. 中国物理B, 2021, 30(8): 80203-080203.
[15]	Liang-An Huo(霍良安), Ya-Fang Dong(董雅芳), and Ting-Ting Lin(林婷婷). Dynamics of a stochastic rumor propagation model incorporating media coverage and driven by Lévy noise[J]. 中国物理B, 2021, 30(8): 80201-080201.

A new method to obtain approximate symmetry of nonlinear evolution equation from perturbations

A new method to obtain approximate symmetry of nonlinear evolution equation from perturbations

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 0