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Volume 97 - 1984

Contents

Page 2 of 2

Research Article

  • The Froude number for solitary waves

  • J. B. McLeod
  • Published online by Cambridge University Press:
    14 November 2011, pp. 193-197

  • The paper is concerned with the problem of a solitary wave moving with constant form and constant velocity c on the surface of an incompressible, inviscid fluid over a horizontal bottom. The motion is assumed to be two-dimensional and irrotational, and if h is the depth of the fluid at infinity and g the acceleration due to gravity, then the Froude number F is defined by

    The result that F>1 has recently been proved by Amick and Toland by means of a long and complicated argument. Here we give a short and simple one.

  • On positive differential operators (deficiency indices, factorization, perturbations)

  • F. S. Rofe-Beketov
  • Published online by Cambridge University Press:
    14 November 2011, pp. 247-257

  • A short survey is given of some recent results. The perturbations and stability of discrete spectrum and the problems of resolvent convergence of densely or non-densely defined elliptic differential operators are considered. The Courant theorem on variations of the domain is generalized. In connection with Berezanskiy's theorem on essential self-adjointness, the test for the finite velocity of propagation is extended. The Frobenius and the Krein-Heinz-Rellich factorization theorems and the Etgen Pawlowski oscillation criterion are generalized for equations of any order with operator-valued coefficients. Brusentsev's recent example of a two term fourth order differential operator with deficiency index 4 is discussed.

Index

Front matter

  • PRM volume 97 Cover and Front matter

  • Published online by Cambridge University Press:
    14 November 2011, pp. f1-f5
    • Article
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Back matter

  • PRM volume 97 Cover and Back matter

  • Published online by Cambridge University Press:
    14 November 2011, pp. b1-b2
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Page 2 of 2