Regularity of Stokes Waves in Hardy Spaces and in Spaces of Distributions (2007)
J. F. Toland, Claverton Down, Bath Ba Ay
This paper deals with some functional-analytic questions which arise when the Stokes-wave problem, for the free boundary of a steady irrotational water wave, is formulated as a quadratic equation for...
J.F. Toland, D. Williams, Bath Ba Ay
The Schur sufficiency condition for boundedness of any integral operator with non-negative kernel between L 2 -spaces is deduced from an observation, Proposition 1.2, about the central role played by...
Self-adjoint Operators and Cones (2007)
Suppose that K is a cone in a real Hilbert space H with K ? = f0g and that A : H ! H is a self-adjoint operator which maps K into itself. If kAk is an eigenvalue of A, it is shown that it has an...
On the Symmetry Theory for Stokes Waves of Finite and Infinite Depth (2007)
older continuous derivative (that is, 2 C 1; (R) for some 2 (0; 1)) and let S() = f(x; (x)) : x 2 Rg and ) = f(x; y) : 0 < y < (x); x 2 Rg: Now let C() denote the set of all innitely...
this paper we give complete proofs of the main results about the Stokeswave problem starting with its basic formulation as a free boundary problem for a harmonic function in an unknown domain in the...
Nash-Moser Theory for Standing Water Waves (2007)
Unlike progressive (or steady) Stokes waves, standing waves are a truly timedependent phenomenon in the sense that they can not be regarded as stationary relative to a moving reference frame and we...
The Index Change and Global Bifurcation for Flows with a First Integral (2006)
The existence, continuation and bifurcation of solutions of fixed period τ of one-parameter families of ordinary differential equations with a first integral may be studied using the topological...
Degree Theory for Orbits of Prescribed Period of Flows with a First Integral (2006)
A new degree function, defined for flows which have a continuously differentiable first integral, counts, algebraically, the number of orbits of fixed period τ in a set Ω. The degree takes...
Standing waves on an infinitely deep perfect fluid under gravity (2005)
Iooss, Gérard, Plotnikov, P.I., Toland, J.F.
The existence of two-dimensional standing-waves on the surface of an infinitely deep perfect fluid under gravity is established....
Standing waves on an infinitely deep perfect fluid under gravity (2005)
Iooss, Gérard, Plotnikov, P.I., Toland, J.F.
The existence of two-dimensional standing-waves on the surface of an infinitely deep perfect fluid under gravity is established....
Standing waves on an infinitely deep perfect fluid under gravity (2005)
Iooss, Gérard, Plotnikov, P.I., Toland, J.F.
The existence of two-dimensional standing-waves on the surface of an infinitely deep perfect fluid under gravity is established....
Standing waves on an infinitely deep perfect fluid under gravity (2005)
Iooss, Gérard, Plotnikov, P.I., Toland, J.F.
The existence of two-dimensional standing-waves on the surface of an infinitely deep perfect fluid under gravity is established....
Finite-Amplitude Solitary Water Waves. (2002)
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,...
On Periodic Water-Waves and Their Convergence to Solitary Waves in the Long-Wave Limit. (2002)
A detailed discussion of Nekrasov's approach to the steady water-wave problems leads to a new integral equation formulation of the periodic problem. This development allows the adaptation of the...
Surface Water Waves as Saddle Points of the Energy (2001)
B. Buffoni, É. Séré, J. F. Toland
By applying the mountain-pass lemma to an energy functional, we establish the existence of two-dimensional water waves on the surface of an infinitely deep ocean in a constant gravity field. The...
A Variational Theory of Stokes Waves and their Sub-Harmonic Bifurcations (1998)
Sub-harmonic Bifurcations, B. Buffoni, E. N. Dancer, J. F. Toland
A formulation of the classical hydrodynamicproblem of periodic waves on the free-surface of an infinitely deep, irrotational flow, which moves steadily under the influence of gravity and possibly...
Sur les ondes de Stokes et une conjecture de Levi-Civita (1998)
Buffoni Dancer Toland, B. Buffoni, E. N. Dancer, J. F. Toland
In his work [5] on Stokes waves (stationary periodic gravity-waves), Levi-Civita conjectured that, for any given propagation speed c ? 0, the wave-lengths are not larger than 2c 2 =g, where g ? 0 is...
B. Buffoni, M. D. Groves, J. F. Toland
This paper considers the existence of solitary-wave solutions of the classical water-wave problem in the presence of surface tension. A region of Bond number-Froude number parameter space close to...
Bifurcation and coalescence of a plethora of homoclinic orbits for a Hamiltonian system (1994)
B. Buffoni, A. R. Champneys, J. F. Toland, Claverton Down, Ba Ay, U \gamma U
This is a further study of the set of homoclinic solutions (i.e. non-zero solutions asymptotic to 0 as jxj !1) of the reversible Hamiltonian system u iv + Pu 00 + u \Gamma u 2 = 0: () The present...
Uniqueness of Benjamin's Solitary-Wave Solution of the Benjamin-Ono Equation (1991)
It is shown, using the maximum principle for hear elliptic equations, estimates on a Green's function, and the Cauchy-Riemann equations, that every nonconstant supercritical solitary-wave solution of...