Solitary waves and shock waves for the perturbed Kawahara equation

Lakhveer Kaur; Ahmed H. Arnous; Ibrahim Zeghaiton Chaloob; Ahmed Shaker Mahmood; Aymen Mohammed Khodayer Al-Dulaimi; Anjan Biswas

doi:10.1016/j.exco.2026.100214

Solitary waves and shock waves for the perturbed Kawahara equation

Lakhveer Kaur
, Ahmed H. Arnous
, Ibrahim Zeghaiton Chaloob
, Ahmed Shaker Mahmood
, Aymen Mohammed Khodayer Al-Dulaimi
, Anjan Biswas^*

^*Corresponding author for this work

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

Abstract

This paper retrieves singular soliyary waves and shock wave solutions to the perturbed Kawahara equation that describes shallow water wave dynamics. The generalized (Formula presented) -expansion methodology is implemented to recover these solutions. The solitary waves appear with parameter constraints that are enlisted for the existence of such solutions.

Original language	English
Article number	100214
Journal	Examples and Counterexamples
Volume	9
DOIs	https://doi.org/10.1016/j.exco.2026.100214
Publication status	Published - Jun 2026
Externally published	Yes

Keywords

35C08
76B25
Integrability
Parameter constraints

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10.1016/j.exco.2026.100214

Cite this

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title = "Solitary waves and shock waves for the perturbed Kawahara equation",

abstract = "This paper retrieves singular soliyary waves and shock wave solutions to the perturbed Kawahara equation that describes shallow water wave dynamics. The generalized (Formula presented) -expansion methodology is implemented to recover these solutions. The solitary waves appear with parameter constraints that are enlisted for the existence of such solutions.",

keywords = "35C08, 76B25, Integrability, Parameter constraints",

author = "Lakhveer Kaur and Arnous, \{Ahmed H.\} and Chaloob, \{Ibrahim Zeghaiton\} and Mahmood, \{Ahmed Shaker\} and Al-Dulaimi, \{Aymen Mohammed Khodayer\} and Anjan Biswas",

note = "Publisher Copyright: {\textcopyright} 2026 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license. http://creativecommons.org/licenses/by-nc-nd/4.0/",

year = "2026",

month = jun,

doi = "10.1016/j.exco.2026.100214",

language = "English",

volume = "9",

journal = "Examples and Counterexamples",

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publisher = "Elsevier B.V.",

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AU - Kaur, Lakhveer

AU - Arnous, Ahmed H.

AU - Chaloob, Ibrahim Zeghaiton

AU - Mahmood, Ahmed Shaker

AU - Al-Dulaimi, Aymen Mohammed Khodayer

AU - Biswas, Anjan

PY - 2026/6

Y1 - 2026/6

N2 - This paper retrieves singular soliyary waves and shock wave solutions to the perturbed Kawahara equation that describes shallow water wave dynamics. The generalized (Formula presented) -expansion methodology is implemented to recover these solutions. The solitary waves appear with parameter constraints that are enlisted for the existence of such solutions.

AB - This paper retrieves singular soliyary waves and shock wave solutions to the perturbed Kawahara equation that describes shallow water wave dynamics. The generalized (Formula presented) -expansion methodology is implemented to recover these solutions. The solitary waves appear with parameter constraints that are enlisted for the existence of such solutions.

KW - 35C08

KW - 76B25

KW - Integrability

KW - Parameter constraints

UR - https://www.scopus.com/pages/publications/105034343307

U2 - 10.1016/j.exco.2026.100214

DO - 10.1016/j.exco.2026.100214

M3 - Article

AN - SCOPUS:105034343307

SN - 2666-657X

VL - 9

JO - Examples and Counterexamples

JF - Examples and Counterexamples

M1 - 100214

ER -

Solitary waves and shock waves for the perturbed Kawahara equation

Abstract

Keywords

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