Home > Research > Publications & Outputs > An obstruction to the integrability of a class ...

Research

Links

Text available via DOI:

View graph of relations

An obstruction to the integrability of a class of non-linear wave equations by 1-stable cartan characteristics

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Published

Standard

An obstruction to the integrability of a class of non-linear wave equations by 1-stable cartan characteristics. / Fackerell, E. D.; Hartley, D. H.; Tucker, Robin.
In: Journal of Differential Equations, Vol. 115, No. 1, 01.01.1995, p. 153-165.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Fackerell, ED, Hartley, DH & Tucker, R 1995, 'An obstruction to the integrability of a class of non-linear wave equations by 1-stable cartan characteristics', Journal of Differential Equations, vol. 115, no. 1, pp. 153-165. https://doi.org/10.1006/jdeq.1995.1009

APA

Fackerell, E. D., Hartley, D. H., & Tucker, R. (1995). An obstruction to the integrability of a class of non-linear wave equations by 1-stable cartan characteristics. Journal of Differential Equations, 115(1), 153-165. https://doi.org/10.1006/jdeq.1995.1009

Vancouver

Fackerell ED, Hartley DH, Tucker R. An obstruction to the integrability of a class of non-linear wave equations by 1-stable cartan characteristics. Journal of Differential Equations. 1995 Jan 1;115(1):153-165. doi: 10.1006/jdeq.1995.1009

Author

Fackerell, E. D. ; Hartley, D. H. ; Tucker, Robin. / An obstruction to the integrability of a class of non-linear wave equations by 1-stable cartan characteristics. In: Journal of Differential Equations. 1995 ; Vol. 115, No. 1. pp. 153-165.

Bibtex

@article{c1c95d8116b047b2b660a2d5caa51963,
title = "An obstruction to the integrability of a class of non-linear wave equations by 1-stable cartan characteristics",
abstract = "We examine in detail the Cauchy problem for a class of non-linear hyperbolic equations in two independent variables. This class is motivated by the analysis of the dynamics of a line of non-linearly coupled particles by Fermi, Pasta, and Ulam and extends the recent investigation of this problem by Gardner and Kamran. We find conditions for the existence of a 1-stable Cartan characteristic of a Pfaffian exterior differential system whose integral curves provide a solution to the Cauchy problem. The same obstruction to involution is exposed in Darboux′s method of integration and the two approaches are compared. A class of particular solutions to the obstruction is constructed.",
author = "Fackerell, {E. D.} and Hartley, {D. H.} and Robin Tucker",
year = "1995",
month = jan,
day = "1",
doi = "10.1006/jdeq.1995.1009",
language = "English",
volume = "115",
pages = "153--165",
journal = "Journal of Differential Equations",
issn = "0022-0396",
publisher = "Academic Press Inc.",
number = "1",

}

RIS

TY - JOUR

T1 - An obstruction to the integrability of a class of non-linear wave equations by 1-stable cartan characteristics

AU - Fackerell, E. D.

AU - Hartley, D. H.

AU - Tucker, Robin

PY - 1995/1/1

Y1 - 1995/1/1

N2 - We examine in detail the Cauchy problem for a class of non-linear hyperbolic equations in two independent variables. This class is motivated by the analysis of the dynamics of a line of non-linearly coupled particles by Fermi, Pasta, and Ulam and extends the recent investigation of this problem by Gardner and Kamran. We find conditions for the existence of a 1-stable Cartan characteristic of a Pfaffian exterior differential system whose integral curves provide a solution to the Cauchy problem. The same obstruction to involution is exposed in Darboux′s method of integration and the two approaches are compared. A class of particular solutions to the obstruction is constructed.

AB - We examine in detail the Cauchy problem for a class of non-linear hyperbolic equations in two independent variables. This class is motivated by the analysis of the dynamics of a line of non-linearly coupled particles by Fermi, Pasta, and Ulam and extends the recent investigation of this problem by Gardner and Kamran. We find conditions for the existence of a 1-stable Cartan characteristic of a Pfaffian exterior differential system whose integral curves provide a solution to the Cauchy problem. The same obstruction to involution is exposed in Darboux′s method of integration and the two approaches are compared. A class of particular solutions to the obstruction is constructed.

U2 - 10.1006/jdeq.1995.1009

DO - 10.1006/jdeq.1995.1009

M3 - Journal article

VL - 115

SP - 153

EP - 165

JO - Journal of Differential Equations

JF - Journal of Differential Equations

SN - 0022-0396

IS - 1

ER -