Periodic and rational solutions of modified Korteweg-de Vries equation

Amdad Chowdury; Adrian Ankiewicz; Nail Akhmediev

doi:10.1140/epjd/e2016-70033-9

Periodic and rational solutions of modified Korteweg-de Vries equation

Amdad Chowdury^*, Adrian Ankiewicz, Nail Akhmediev

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

33 Citations (Scopus)

Abstract

Abstract: We present closed form periodic solutions of the integrable modified Korteweg-de Vriesequation (mKdV). By using a Darboux transformation, we derive first-and second-orderdoubly-periodic lattice-like solutions. We explicitly derive first-and second-orderrational solutions as limiting cases of periodic solutions. We have also found thedegenerate solution which corresponds to the equal eigenvalue case. Among the second-ordersolutions, we single out the doubly-localized high peak solution on a constant backgroundwith an infinitely extended trough. This solution plays the role of a rogue wave of themKdV equation. Graphical abstract: [Figure not available: see fulltext.]

Original language	English
Article number	104
Pages (from-to)	1-7
Number of pages	7
Journal	European Physical Journal D
Volume	70
Issue number	5
DOIs	https://doi.org/10.1140/epjd/e2016-70033-9
Publication status	Published - 1 May 2016

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title = "Periodic and rational solutions of modified Korteweg-de Vries equation",

abstract = "Abstract: We present closed form periodic solutions of the integrable modified Korteweg-de Vriesequation (mKdV). By using a Darboux transformation, we derive first-and second-orderdoubly-periodic lattice-like solutions. We explicitly derive first-and second-orderrational solutions as limiting cases of periodic solutions. We have also found thedegenerate solution which corresponds to the equal eigenvalue case. Among the second-ordersolutions, we single out the doubly-localized high peak solution on a constant backgroundwith an infinitely extended trough. This solution plays the role of a rogue wave of themKdV equation. Graphical abstract: [Figure not available: see fulltext.]",

keywords = "Nonlinear Dynamics",

author = "Amdad Chowdury and Adrian Ankiewicz and Nail Akhmediev",

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T1 - Periodic and rational solutions of modified Korteweg-de Vries equation

AU - Chowdury, Amdad

AU - Ankiewicz, Adrian

AU - Akhmediev, Nail

PY - 2016/5/1

Y1 - 2016/5/1

N2 - Abstract: We present closed form periodic solutions of the integrable modified Korteweg-de Vriesequation (mKdV). By using a Darboux transformation, we derive first-and second-orderdoubly-periodic lattice-like solutions. We explicitly derive first-and second-orderrational solutions as limiting cases of periodic solutions. We have also found thedegenerate solution which corresponds to the equal eigenvalue case. Among the second-ordersolutions, we single out the doubly-localized high peak solution on a constant backgroundwith an infinitely extended trough. This solution plays the role of a rogue wave of themKdV equation. Graphical abstract: [Figure not available: see fulltext.]

AB - Abstract: We present closed form periodic solutions of the integrable modified Korteweg-de Vriesequation (mKdV). By using a Darboux transformation, we derive first-and second-orderdoubly-periodic lattice-like solutions. We explicitly derive first-and second-orderrational solutions as limiting cases of periodic solutions. We have also found thedegenerate solution which corresponds to the equal eigenvalue case. Among the second-ordersolutions, we single out the doubly-localized high peak solution on a constant backgroundwith an infinitely extended trough. This solution plays the role of a rogue wave of themKdV equation. Graphical abstract: [Figure not available: see fulltext.]

KW - Nonlinear Dynamics

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DO - 10.1140/epjd/e2016-70033-9

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SP - 1

EP - 7

JO - European Physical Journal D

JF - European Physical Journal D

IS - 5

M1 - 104

ER -

Periodic and rational solutions of modified Korteweg-de Vries equation

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