The bifurcation and secondary bifurcation of capillary-gravity waves

J. R. Toland; M. C. W. Jones

The bifurcation and secondary bifurcation of capillary-gravity waves

J. R. Toland, M. C. W. Jones

Department of Mathematical Sciences

Cent for Mathematical Analysis

Research output: Contribution to journal › Article › peer-review

Abstract

The bifurcation and secondary bifurcation of capillary-gravity waves is analyzed when the surface tension is close to or equal to a value where the eignespace of the critical phase speed has multiplicity two. The existence and multiplicity of solutions is seen, via the implicit function theorem, to be a special case of the secondary bifurcation phenomena, which occur when a double eigenvalue splits, under perturbation, into two simple eigenvalues in the presence of a symmetry in the problem.

Original language	English
Pages (from-to)	391-417
Number of pages	27
Journal	Proceedings of The Royal Society of London, Series A: Mathematical and Physical Sciences
Volume	399
Issue number	1817
Publication status	Published - 8 Jun 1985

ASJC Scopus subject areas

General Mathematics
General Engineering
General Physics and Astronomy

Cite this

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title = "The bifurcation and secondary bifurcation of capillary-gravity waves",

abstract = "The bifurcation and secondary bifurcation of capillary-gravity waves is analyzed when the surface tension is close to or equal to a value where the eignespace of the critical phase speed has multiplicity two. The existence and multiplicity of solutions is seen, via the implicit function theorem, to be a special case of the secondary bifurcation phenomena, which occur when a double eigenvalue splits, under perturbation, into two simple eigenvalues in the presence of a symmetry in the problem.",

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AU - Jones, M. C. W.

PY - 1985/6/8

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N2 - The bifurcation and secondary bifurcation of capillary-gravity waves is analyzed when the surface tension is close to or equal to a value where the eignespace of the critical phase speed has multiplicity two. The existence and multiplicity of solutions is seen, via the implicit function theorem, to be a special case of the secondary bifurcation phenomena, which occur when a double eigenvalue splits, under perturbation, into two simple eigenvalues in the presence of a symmetry in the problem.

AB - The bifurcation and secondary bifurcation of capillary-gravity waves is analyzed when the surface tension is close to or equal to a value where the eignespace of the critical phase speed has multiplicity two. The existence and multiplicity of solutions is seen, via the implicit function theorem, to be a special case of the secondary bifurcation phenomena, which occur when a double eigenvalue splits, under perturbation, into two simple eigenvalues in the presence of a symmetry in the problem.

UR - https://www.scopus.com/pages/publications/0022421262

M3 - Article

AN - SCOPUS:0022421262

SN - 0080-4630

VL - 399

SP - 391

EP - 417

JO - Proceedings of The Royal Society of London, Series A: Mathematical and Physical Sciences

JF - Proceedings of The Royal Society of London, Series A: Mathematical and Physical Sciences

IS - 1817

ER -

The bifurcation and secondary bifurcation of capillary-gravity waves

Abstract

ASJC Scopus subject areas

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