Generalized solitary waves in a finite-difference Korteweg-de Vries equation

N. Joshi, C. J. Lustri

Research output: Contribution to journalArticleResearchpeer-review

Abstract

Generalized solitary waves with exponentially small nondecaying far field oscillations have been studied in a range of singularly perturbed differential equations, including higher order Korteweg-de Vries (KdV) equations. Many of these studies used exponential asymptotics to compute the behavior of the oscillations, revealing that they appear in the solution as special curves known as Stokes lines are crossed. Recent studies have identified similar behavior in solutions to difference equations. Motivated by these studies, the seventh-order KdV and a hierarchy of higher order KdV equations are investigated, identifying conditions which produce generalized solitary wave solutions. These results form a foundation for the study of infinite-order differential equations, which are used as a model for studying lattice equations. Finally, a lattice KdV equation is generated using finite-difference discretization, in which a lattice generalized solitary wave solution is found.

LanguageEnglish
Pages359-384
Number of pages26
JournalStudies in Applied Mathematics
Volume142
Issue number3
Early online date10 Jan 2019
DOIs
Publication statusPublished - Apr 2019

Fingerprint

Korteweg-de Vries equation
Solitary Waves
Solitons
Korteweg-de Vries Equation
Difference equation
Finite Difference
Higher order equation
Solitary Wave Solution
Differential equations
Exponential Asymptotics
Oscillation
Differential equation
Difference equations
Singularly Perturbed
Far Field
Stokes
Discretization
Curve
Line
Range of data

Keywords

  • asymptotic analysis
  • solitons and integrable systems

Cite this

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Generalized solitary waves in a finite-difference Korteweg-de Vries equation. / Joshi, N.; Lustri, C. J.

In: Studies in Applied Mathematics, Vol. 142, No. 3, 04.2019, p. 359-384.

Research output: Contribution to journalArticleResearchpeer-review

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