Shock Wave and Singular Solitary Wave Perturbation with Gardners Equation Having Dispersion Triplet

Lakhveer Kaur; Anjan Biswas; Ahmed H. Arnous; Yakup Yildirim; Luminita Moraru; Mushin J. Jweeg

doi:10.37256/cm.6320256903

Shock Wave and Singular Solitary Wave Perturbation with Gardners Equation Having Dispersion Triplet

Lakhveer Kaur
, Anjan Biswas
, Ahmed H. Arnous
, Yakup Yildirim^*
, Luminita Moraru
, Mushin J. Jweeg

^*Corresponding author for this work

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

2 Citations (Scopus)

Abstract

The current paper recovers the shock wave and solitary wave solutions to the well-known Korteweg-de Vries-modified Korteweg-de Vries (KdV-mKdV) equation with perturbation terms that is alternately known as the Gardners equation. The integration scheme adopted in this work to retrieve such solutions is the G^′/G-expansion. The results appear with parameter constraints for the existence of such waves and these are also presented.

Original language	English
Pages (from-to)	3743-3762
Number of pages	20
Journal	Contemporary Mathematics (Singapore)
Volume	6
Issue number	3
DOIs	https://doi.org/10.37256/cm.6320256903
Publication status	Published - 2025
Externally published	Yes

Keywords

Gardners equation
shock wave
solitary wave

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10.37256/cm.6320256903

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title = "Shock Wave and Singular Solitary Wave Perturbation with Gardners Equation Having Dispersion Triplet",

abstract = "The current paper recovers the shock wave and solitary wave solutions to the well-known Korteweg-de Vries-modified Korteweg-de Vries (KdV-mKdV) equation with perturbation terms that is alternately known as the Gardners equation. The integration scheme adopted in this work to retrieve such solutions is the G′/G-expansion. The results appear with parameter constraints for the existence of such waves and these are also presented.",

keywords = "Gardners equation, shock wave, solitary wave",

author = "Lakhveer Kaur and Anjan Biswas and Arnous, \{Ahmed H.\} and Yakup Yildirim and Luminita Moraru and Jweeg, \{Mushin J.\}",

note = "Publisher Copyright: {\textcopyright} 2025 Yakup Yildirim, et al.",

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AU - Kaur, Lakhveer

AU - Biswas, Anjan

AU - Arnous, Ahmed H.

AU - Yildirim, Yakup

AU - Moraru, Luminita

AU - Jweeg, Mushin J.

PY - 2025

Y1 - 2025

N2 - The current paper recovers the shock wave and solitary wave solutions to the well-known Korteweg-de Vries-modified Korteweg-de Vries (KdV-mKdV) equation with perturbation terms that is alternately known as the Gardners equation. The integration scheme adopted in this work to retrieve such solutions is the G′/G-expansion. The results appear with parameter constraints for the existence of such waves and these are also presented.

AB - The current paper recovers the shock wave and solitary wave solutions to the well-known Korteweg-de Vries-modified Korteweg-de Vries (KdV-mKdV) equation with perturbation terms that is alternately known as the Gardners equation. The integration scheme adopted in this work to retrieve such solutions is the G′/G-expansion. The results appear with parameter constraints for the existence of such waves and these are also presented.

KW - Gardners equation

KW - shock wave

KW - solitary wave

UR - https://www.scopus.com/pages/publications/105009163835

U2 - 10.37256/cm.6320256903

DO - 10.37256/cm.6320256903

M3 - Article

AN - SCOPUS:105009163835

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VL - 6

SP - 3743

EP - 3762

JO - Contemporary Mathematics (Singapore)

JF - Contemporary Mathematics (Singapore)

IS - 3

ER -

Shock Wave and Singular Solitary Wave Perturbation with Gardners Equation Having Dispersion Triplet

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Keywords

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