Numerical solutions of nonlinear wave equations

Journal Article · Fri Jan 01 04:00:00 EST 1999 · Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

DOI:https://doi.org/10.1103/PhysRevE.59.1274· OSTI ID:295536

Kouri, D J; Zhang, D S; Wei, G W ^[1]; Konshak, T; Hoffman, D K ^[2]

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1. Department of Chemistry and Department of Physics, University of Houston, Houston, Texas 77204-5641 (United States)
2. Department of Chemistry and Ames Laboratory, Iowa State University, Ames, Iowa 50011 (United States)

Accurate, stable numerical solutions of the (nonlinear) sine-Gordon equation are obtained with particular consideration of initial conditions that are exponentially close to the phase space homoclinic manifolds. Earlier local, grid-based numerical studies have encountered difficulties, including numerically induced chaos for such initial conditions. The present results are obtained using the recently reported distributed approximating functional method for calculating spatial derivatives to high accuracy and a simple, explicit method for the time evolution. The numerical solutions are chaos-free for the same conditions employed in previous work that encountered chaos. Moreover, stable results that are free of homoclinic-orbit crossing are obtained even when initial conditions are within 10{sup {minus}7} of the phase space separatrix value {pi}. It also is found that the present approach yields extremely accurate solutions for the Korteweg{endash}de Vries and nonlinear Schr{umlt o}dinger equations. Our results support Ablowitz and co-workers{close_quote} conjecture that ensuring high accuracy of spatial derivatives is more important than the use of symplectic time integration schemes for solving solitary wave equations. {copyright} {ital 1999} {ital The American Physical Society}

• OSTI ID: 295536
• Journal Information: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics Journal Issue: 1 Vol. 59; ISSN 1063-651X; ISSN PLEEE8
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
KORTEWEG-DE VRIES EQUATION
NUMERICAL ANALYSIS
NUMERICAL SOLUTION
SCHROEDINGER EQUATION
SINE-GORDON EQUATION
STABILITY
WAVE EQUATIONS