摘要:

Singularly perturbed linear Volterra or Fredholm integral equations with kernels possessing jump discontinuities in a derivative are discussed within the framework of [6]. An intriguing and remarkable feature of such equations is that in general the leading order outer solution does not satisfy the unperturbed integral equation. Moreover, the solution usually exhibits large amplitude boundary layer behavior at one or both endpoints. Our perturbation technique, which is based on an efficient asymptotic splitting of the integral equation, clearly reveals the rich asymptotic solution structure for this class of equations.

ISSN:0022-2526    

DOI:10.1002/sapm19939011

年代:1993

数据来源: WILEY

摘要:

Using a multi‐scale perturbation expansion we reconsider the slowly varying solitary wave asymptotic solution of the perturbed Korteweg‐de Vries equation. The well‐known results for the variation of the solitary‐wave amplitude and the accompanying trailing tail are recovered. Here the analysis is carried through to second order so as to determine a general expression for the first‐order speed correction. The result obtained here generalizes and improves previou

ISSN:0022-2526    

DOI:10.1002/sapm199390175

年代:1993

数据来源: WILEY

摘要:

A simple method is used to derive the exponentially small oscillatory tails of solitons when the Korteweg‐de Vries equation is perturbed with a higher‐order dispersive term. A physical interpretation of the results is given, and several possible extensions to the problem are propo

ISSN:0022-2526    

DOI:10.1002/sapm199390187

年代:1993

数据来源: WILEY