A new perturbative approach to nonlinear partial differential equations

Journal Article · Fri Nov 01 00:00:00 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), Vol. 32:11; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

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