HYBRID SOLITARY WAVES AND SHOCK WAVES FOR DOUBLE–LAYERED FLUID FLOW WITH DISPERSION TRIPLET: ZAREMAOGHADDAM AND GEAR–GRIMSHAW MODELS (mKdV EQUATION)

Lakhveer Kaur; O. González-Gaxiola; Ahmed H. Arnous; Husham M. Ahmed; Haitham Alqahtani; Anjan Biswas

doi:10.26565/2312-4334-2026-1-07

HYBRID SOLITARY WAVES AND SHOCK WAVES FOR DOUBLE–LAYERED FLUID FLOW WITH DISPERSION TRIPLET: ZAREMAOGHADDAM AND GEAR–GRIMSHAW MODELS (mKdV EQUATION)

Lakhveer Kaur
, O. González-Gaxiola^*
, Ahmed H. Arnous
, Husham M. Ahmed
, Haitham Alqahtani
, Anjan Biswas

^*Corresponding author for this work

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

Abstract

The current paper recovers hybrid solitary waves for double–layered shallow water waves with the basic platform being the mKdV equation. The selected models are the Zaremaoghaddam equation and the Gear–Grimshaw equation. The integration algorithm adopted is the generalized exponential differential function method. This yields hybrid waves that emerge from solitary waves, shock waves and the singular solitary waves. The existence criteria for such waves are also presented as parameter constraints.

Original language	English
Pages (from-to)	88-104
Number of pages	17
Journal	East European Journal of Physics
Volume	2026
Issue number	1
DOIs	https://doi.org/10.26565/2312-4334-2026-1-07
Publication status	Published - 14 Mar 2026
Externally published	Yes

Keywords

Gear–Grimshaw equation
Hybrid
Integrability
Parameter constraints
mKdV equation

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10.26565/2312-4334-2026-1-07

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title = "HYBRID SOLITARY WAVES AND SHOCK WAVES FOR DOUBLE{\textendash}LAYERED FLUID FLOW WITH DISPERSION TRIPLET: ZAREMAOGHADDAM AND GEAR{\textendash}GRIMSHAW MODELS (mKdV EQUATION)",

abstract = "The current paper recovers hybrid solitary waves for double{\textendash}layered shallow water waves with the basic platform being the mKdV equation. The selected models are the Zaremaoghaddam equation and the Gear{\textendash}Grimshaw equation. The integration algorithm adopted is the generalized exponential differential function method. This yields hybrid waves that emerge from solitary waves, shock waves and the singular solitary waves. The existence criteria for such waves are also presented as parameter constraints.",

keywords = "Gear{\textendash}Grimshaw equation, Hybrid, Integrability, Parameter constraints, mKdV equation",

author = "Lakhveer Kaur and O. Gonz{\'a}lez-Gaxiola and Arnous, \{Ahmed H.\} and Ahmed, \{Husham M.\} and Haitham Alqahtani and Anjan Biswas",

note = "Publisher Copyright: {\textcopyright} L. Kaur, O. Gonz{\'a}lez{\textendash}Gaxiola, A.H. Arnous, H.M. Ahmed, H. Alqahtani, A. Biswas, 2026.",

year = "2026",

month = mar,

day = "14",

doi = "10.26565/2312-4334-2026-1-07",

language = "English",

volume = "2026",

pages = "88--104",

journal = "East European Journal of Physics",

issn = "2312-4334",

publisher = "Karazin Kharkiv National University",

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TY - JOUR

T1 - HYBRID SOLITARY WAVES AND SHOCK WAVES FOR DOUBLE–LAYERED FLUID FLOW WITH DISPERSION TRIPLET

T2 - ZAREMAOGHADDAM AND GEAR–GRIMSHAW MODELS (mKdV EQUATION)

AU - Kaur, Lakhveer

AU - González-Gaxiola, O.

AU - Arnous, Ahmed H.

AU - Ahmed, Husham M.

AU - Alqahtani, Haitham

AU - Biswas, Anjan

N1 - Publisher Copyright: © L. Kaur, O. González–Gaxiola, A.H. Arnous, H.M. Ahmed, H. Alqahtani, A. Biswas, 2026.

PY - 2026/3/14

Y1 - 2026/3/14

N2 - The current paper recovers hybrid solitary waves for double–layered shallow water waves with the basic platform being the mKdV equation. The selected models are the Zaremaoghaddam equation and the Gear–Grimshaw equation. The integration algorithm adopted is the generalized exponential differential function method. This yields hybrid waves that emerge from solitary waves, shock waves and the singular solitary waves. The existence criteria for such waves are also presented as parameter constraints.

AB - The current paper recovers hybrid solitary waves for double–layered shallow water waves with the basic platform being the mKdV equation. The selected models are the Zaremaoghaddam equation and the Gear–Grimshaw equation. The integration algorithm adopted is the generalized exponential differential function method. This yields hybrid waves that emerge from solitary waves, shock waves and the singular solitary waves. The existence criteria for such waves are also presented as parameter constraints.

KW - Gear–Grimshaw equation

KW - Hybrid

KW - Integrability

KW - Parameter constraints

KW - mKdV equation

UR - https://www.scopus.com/pages/publications/105033259167

U2 - 10.26565/2312-4334-2026-1-07

DO - 10.26565/2312-4334-2026-1-07

M3 - Article

AN - SCOPUS:105033259167

SN - 2312-4334

VL - 2026

SP - 88

EP - 104

JO - East European Journal of Physics

JF - East European Journal of Physics

IS - 1

ER -

HYBRID SOLITARY WAVES AND SHOCK WAVES FOR DOUBLE–LAYERED FLUID FLOW WITH DISPERSION TRIPLET: ZAREMAOGHADDAM AND GEAR–GRIMSHAW MODELS (mKdV EQUATION)

Abstract

Keywords

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