A new perturbative approach to nonlinear partial differential equations

Journal Article · Thu Oct 31 23:00:00 EST 1991 · Journal of Mathematical Physics (New York); (United States)

DOI:https://doi.org/10.1063/1.529047· OSTI ID:5022145

Bender, C M; Boettcher, S ^[1]; Milton, K A ^[2]

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1. Department of Physics, Washington University, St. Louis, Missouri (USA)
2. Department of Physics and Astronomy, University of Oklahoma, Norman, Oklahoma (USA)

This paper shows how to solve some nonlinear wave equations as perturbation expansions in powers of a parameter that expresses the degree of nonlinearity. For the case of the Burgers equation {ital u}{sub {ital t}}+{ital uu}{sub {ital x}}={ital u}{sub {ital xx}}, the general nonlinear equation {ital u}{sub {ital t}}+{ital u}{sup {delta}}{ital u}{sub {ital x}}={ital u}{sub {ital xx}} is considered and expanded in powers of {delta}. The coefficients of the {delta} series to sixth order in powers of {delta} is determined and Pade summation is used to evaluate the perturbation series for large values of {delta}. The numerical results are accurate and the method is very general; it applies to other well-studied partial differential equations such as the Korteweg--de Vries equation, {ital u}{sub {ital t}}+{ital uu}{sub {ital x}} ={ital u}{sub {ital xxx}}.

• OSTI ID: 5022145
• Journal Information: Journal of Mathematical Physics (New York); (United States), Journal Name: Journal of Mathematical Physics (New York); (United States) Vol. 32:11; ISSN JMAPA; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

657002* -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ACCURACY
DATA
DIFFERENTIAL EQUATIONS
EQUATIONS
INFORMATION
KORTEWEG-DE VRIES EQUATION
NONLINEAR PROBLEMS
NUMERICAL DATA
PARTIAL DIFFERENTIAL EQUATIONS
PERTURBATION THEORY
SERIES EXPANSION
USES
WAVE EQUATIONS