Equivalent construction of the infinitesimal time translation operator in algebraic dynamics algorithm for partial differential evolution equation

We give an equivalent construction of the infinitesimal time translation operator for partial differential evolution equation in the algebraic dynamics algorithm proposed by Shun-Jin Wang and his students. Our construction involves only simple partial differentials and avoids the derivative terms of...

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Bibliographic Details
Published in:Science China. Physics, mechanics & astronomy Vol. 53; no. 8; pp. 1475 - 1480
Main Author: Liu, ChengShi
Format: Journal Article
Language:English
Published: Heidelberg SP Science China Press 01.08.2010
Springer Nature B.V
Subjects:
Algebra
Algorithms
Astronomy
Burgers equation
Classical and Continuum Physics
Complex variables
Construction
Differential equations
Equivalence
Evolutionary computation
Observations and Techniques
Operators (mathematics)
Physics
Physics and Astronomy
Real variables
Research Paper
Schrodinger equation
infinitesimal time translation operator
partial differential evolution equation
algebraic dynamics
ISSN:1674-7348, 1869-1927
Online Access:Get full text
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Summary:We give an equivalent construction of the infinitesimal time translation operator for partial differential evolution equation in the algebraic dynamics algorithm proposed by Shun-Jin Wang and his students. Our construction involves only simple partial differentials and avoids the derivative terms of δ function which appear in the course of computation by means of Wang-Zhang operator. We prove Wang’s equivalent theorem which says that our construction and Wang-Zhang’s are equivalent. We use our construction to deal with several typical equations such as nonlinear advection equation, Burgers equation, nonlinear Schrodinger equation, KdV equation and sine-Gordon equation, and obtain at least second order approximate solutions to them. These equations include the cases of real and complex field variables and the cases of the first and the second order time derivatives.
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ISSN:1674-7348
1869-1927
DOI:10.1007/s11433-010-4051-9