Perturbation Theory for the - Benjamin-Ono Equation.

Abstract

We develop a perturbation theory for the Benjamin-Ono (BO) equation. This perturbation theory is based on the Inverse Scattering Transform for the BO equation which was originally developed by Fokas and Ablowitz and recently refined by Kaup and Matsuno. We find the expressions for the variations of the scattering data with respect to the potential, as well as the dual expression for the variation of the potential in terms of the variations of the scattering data. This allows us to introduce the squared eigenfunctions for the BO equation, whose completeness and orthogonality in both chi- and lambda-spaces we also establish. We consider the two most important applications of the developed machinery. First we present an explicit first-order solution of the BO equation driven by a small perturbation. Second we introduce the Poisson bracket and a set of the canonical action-angle variables for the BO equation and thus demonstrate its complete integrability as a Hamiltonian dynamical system.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Jan 26, 1998
Accession Number
ADA341883

Entities

People

  • D. J. Kaup
  • T. I. Lakoba
  • Y. Matsuno

Organizations

  • Clarkson University

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Analogs
  • Analytic Functions
  • Boundaries
  • Coefficients
  • Continuous Spectra
  • Equations
  • Identities
  • Integral Equations
  • Integrals
  • Internal Waves
  • Inverse Scattering
  • Perturbation Theory
  • Perturbations
  • Scattering
  • Solitons
  • Spectra
  • Waves

Fields of Study

  • Mathematics
  • Physics

Readers

  • Calculus or Mathematical Analysis
  • Wave Propagation and Nonlinear Chaotic Dynamics.

Technology Areas

  • Space