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A direct approach to studying soliton perturbations

R L Herman

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Starting with an integrable nonlinear evolution equation, the author investigates perturbations about a one-soliton solution, through the inversion of a linear equation for the first-order correction to the soliton solution. This inversion differs from past methods, as the proposed method takes place in coordinate space, not spectral space, while it employs some of the tools of inverse scattering theory. The method is applied to the Korteweg-de Vries, nonlinear Schrodinger and sine-Gordon equations. The first-order corrections are then obtained.


PACS

02.30.Jr Partial differential equations

05.45.Yv Solitons

MSC

35Q51 Solitons (See also 37K40)

35Q53 KdV-like equations (Korteweg-de Vries, Burgers, sine-Gordon, sinh-Gordon, etc.) (See also 37K10)

35G25 Initial value problems for nonlinear higher-order PDE, nonlinear evolution equations

Subjects

Mathematical physics

Statistical physics and nonlinear systems

Dates

Issue 12 (21 June 1990)



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