Toland, John 1949
Overview
Works:  16 works in 54 publications in 2 languages and 804 library holdings 

Roles:  Author 
Publication Timeline
.
Most widely held works by
John Toland
Analytic theory of global bifurcation : an introduction by
Boris Buffoni(
Book
)
9 editions published in 2003 in English and held by 435 WorldCat member libraries worldwide
9 editions published in 2003 in English and held by 435 WorldCat member libraries worldwide
Bernoulli freeboundary problems by
E Shargorodsky(
Book
)
11 editions published between 2008 and 2009 in English and held by 266 WorldCat member libraries worldwide
Establishes an equivalence between Bernoulli free boundary problems and a class of equations for realvalued functions of one real variable. The equivalent equations can be written as nonlinear RiemannHilbert problems and the theory of complex Hardy spaces in the unit disc has a central role. A canonical Morse index can be assigned to free boundaries and the Calculus of Variations becomes available as a tool for the study
11 editions published between 2008 and 2009 in English and held by 266 WorldCat member libraries worldwide
Establishes an equivalence between Bernoulli free boundary problems and a class of equations for realvalued functions of one real variable. The equivalent equations can be written as nonlinear RiemannHilbert problems and the theory of complex Hardy spaces in the unit disc has a central role. A canonical Morse index can be assigned to free boundaries and the Calculus of Variations becomes available as a tool for the study
Introduction à la théorie globale des bifurcations by
Boris Buffoni(
Book
)
5 editions published in 2002 in French and held by 65 WorldCat member libraries worldwide
5 editions published in 2002 in French and held by 65 WorldCat member libraries worldwide
On periodic waterwaves and their convergence to solitary waves in the longwave limit by C. J Amick(
Book
)
7 editions published between 1980 and 1981 in English and held by 13 WorldCat member libraries worldwide
A detailed discussion of Nekrasov's approach to the steady waterwave problems leads to a new integral equation formulation of the periodic problem. This development allows the adaptation of the methods of (1) to show the global convergence of periodic waves to solitary waves in the longwave limit. In addition, it is shown how the classical integral equation formulation due to Nekrasove leads, via the Maximum Principle, to new results about qualitative features of periodic waves, for which there has long been a global existence theory (9, 12). (Author)
7 editions published between 1980 and 1981 in English and held by 13 WorldCat member libraries worldwide
A detailed discussion of Nekrasov's approach to the steady waterwave problems leads to a new integral equation formulation of the periodic problem. This development allows the adaptation of the methods of (1) to show the global convergence of periodic waves to solitary waves in the longwave limit. In addition, it is shown how the classical integral equation formulation due to Nekrasove leads, via the Maximum Principle, to new results about qualitative features of periodic waves, for which there has long been a global existence theory (9, 12). (Author)
Finiteamplitude solitary water waves by C. J Amick(
Book
)
5 editions published in 1979 in English and Undetermined and held by 7 WorldCat member libraries worldwide
This paper considers the existence problem for solutions of the free boundary value problem which arises from the question of the existence of solitary gravity waves, moving without changes of form, and with constant velocity, on the surface of ideal fluid in a horizontal canal of finite depth. The analysis imposes no restriction on either the slope or the amplitude of the wave, and we prove that there exists a connected set of solitary waves containing waves of all slope between 0 and pi/6. It is then proved that each of these solitary waves has finite mass, and, as a consequence, that F> 1, where F is the Froude number. This, in turn, tells us that the solitary wave decays faster than exp( alpha abs.val.(x/h), where alpha is an element or (0, alphabar) and 1/alphabar tam(alphbar) = fsquared. Finally, it is shown that, in a certain limit, these solitary waves converge to a solitary stokes wave of greatest height, and the validity of stokes' conjecture for solitary waves is considered, but not resolved. (Author)
5 editions published in 1979 in English and Undetermined and held by 7 WorldCat member libraries worldwide
This paper considers the existence problem for solutions of the free boundary value problem which arises from the question of the existence of solitary gravity waves, moving without changes of form, and with constant velocity, on the surface of ideal fluid in a horizontal canal of finite depth. The analysis imposes no restriction on either the slope or the amplitude of the wave, and we prove that there exists a connected set of solitary waves containing waves of all slope between 0 and pi/6. It is then proved that each of these solitary waves has finite mass, and, as a consequence, that F> 1, where F is the Froude number. This, in turn, tells us that the solitary wave decays faster than exp( alpha abs.val.(x/h), where alpha is an element or (0, alphabar) and 1/alphabar tam(alphbar) = fsquared. Finally, it is shown that, in a certain limit, these solitary waves converge to a solitary stokes wave of greatest height, and the validity of stokes' conjecture for solitary waves is considered, but not resolved. (Author)
The convergence of periodic waves to solitary waves in the long wave limit by
John Toland(
Book
)
5 editions published in 1980 in English and held by 6 WorldCat member libraries worldwide
It is shown that large amplitude solitary waterwaves arise as the limit of periodic waves whose wavelengths increases indefinitely. This results is obtained after a new version of the Nekrasov integral equation for periodic waves has been derived. Its resemblance to the equation for solitary waves (1) leads to this convergence results once the global existence proof for solitary waves given in (1) has been taken into account. (Author)
5 editions published in 1980 in English and held by 6 WorldCat member libraries worldwide
It is shown that large amplitude solitary waterwaves arise as the limit of periodic waves whose wavelengths increases indefinitely. This results is obtained after a new version of the Nekrasov integral equation for periodic waves has been derived. Its resemblance to the equation for solitary waves (1) leads to this convergence results once the global existence proof for solitary waves given in (1) has been taken into account. (Author)
The bifurcation and secondary bifurcation of capillarygravity waves by
John Toland(
Book
)
2 editions published in 1985 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 1985 in English and held by 2 WorldCat member libraries worldwide
Topological Methods for Nonlinear Eigenvalue Problems by
John Toland(
Book
)
2 editions published in 1973 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 1973 in English and held by 2 WorldCat member libraries worldwide
Mathematics of nonlinear systems(
Book
)
1 edition published in 1994 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1994 in English and held by 2 WorldCat member libraries worldwide
Bernuille freeboundary problems by
E Shargorodsky(
Book
)
1 edition published in 2008 in English and held by 1 WorldCat member library worldwide
1 edition published in 2008 in English and held by 1 WorldCat member library worldwide
A Duality Principle for NonConvex Optimisation and the Calculus of Variations by
John Toland(
Book
)
1 edition published in 1976 in English and held by 1 WorldCat member library worldwide
1 edition published in 1976 in English and held by 1 WorldCat member library worldwide
On the stability of rotating heavy chains by
John Toland(
Book
)
1 edition published in 1977 in English and held by 1 WorldCat member library worldwide
1 edition published in 1977 in English and held by 1 WorldCat member library worldwide
Global Bifurcation Theory Via Galerkins Method by
John Toland(
Book
)
1 edition published in 1976 in English and held by 1 WorldCat member library worldwide
1 edition published in 1976 in English and held by 1 WorldCat member library worldwide
A global result applicate to nonlinear Steklov problems by C. A Stuart(
Book
)
1 edition published in 1972 in English and held by 1 WorldCat member library worldwide
1 edition published in 1972 in English and held by 1 WorldCat member library worldwide
Asymptotic Linearity and Nonlinear Eigenvalue Problems 11 by
John Toland(
Book
)
1 edition published in 1975 in English and held by 1 WorldCat member library worldwide
1 edition published in 1975 in English and held by 1 WorldCat member library worldwide
Introduction à la théorie globale des bifurcations by
Boris Buffoni(
)
1 edition published in 2002 in French and held by 0 WorldCat member libraries worldwide
1 edition published in 2002 in French and held by 0 WorldCat member libraries worldwide
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Related Identities
 Buffoni, Boris 1965 Author
 Shargorodsky, E. (Eugene) 1966 Author
 Amick, C. J. Author
 University of WisconsinMadison Mathematics Research Center
 University of Essex
 WISCONSIN UNIVMADISON MATHEMATICS RESEARCH CENTER
 Defense Technical Information Center (U.S.)
 Jones, M. C. W.
 United States Army Research Office
 Ball, J. M. (John MacLeod) 1948
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