Cnoidal Waves, Solitary Waves, Shock Waves and Conservation Laws of the Generalized Cubic Boussinesq-Type Model for Shallow Water Wave Dynamics

Anjan Biswas; Ming Yue Wang; Abdul H. Kara; Yakup Yildirim; Luminita Moraru; Carmelia M. Balanica; Layth Hussein; Anwar Ja’Far Mohamad Jawad

doi:10.37256/cm.6220256389

Cnoidal Waves, Solitary Waves, Shock Waves and Conservation Laws of the Generalized Cubic Boussinesq-Type Model for Shallow Water Wave Dynamics

Anjan Biswas, Ming Yue Wang, Abdul H. Kara, Yakup Yildirim, Luminita Moraru, Carmelia M. Balanica, Layth Hussein, Anwar Ja’Far Mohamad Jawad

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

Abstract

The paper addresses the latest form of Boussinesq equation with generalized form of cubic nonlinearity. The solitary waves are recovered from the model using traveling wave hypothesis. The conservation laws are recovered from the model. The conservation laws are obtained using the method of multipliers. Finally, the complete discriminant method yields shock waves and cnoidal waves as well. The numerical simulations supplement the analytical results.

Original language	English
Pages (from-to)	1973-1987
Number of pages	15
Journal	Contemporary Mathematics (Singapore)
Volume	6
Issue number	2
DOIs	https://doi.org/10.37256/cm.6220256389
Publication status	Published - 2025
Externally published	Yes

Keywords

Boussinesq
conservation laws
shallow water
solitary waves

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10.37256/cm.6220256389

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abstract = "The paper addresses the latest form of Boussinesq equation with generalized form of cubic nonlinearity. The solitary waves are recovered from the model using traveling wave hypothesis. The conservation laws are recovered from the model. The conservation laws are obtained using the method of multipliers. Finally, the complete discriminant method yields shock waves and cnoidal waves as well. The numerical simulations supplement the analytical results.",

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author = "Anjan Biswas and Wang, {Ming Yue} and Kara, {Abdul H.} and Yakup Yildirim and Luminita Moraru and Balanica, {Carmelia M.} and Layth Hussein and Jawad, {Anwar Ja{\textquoteright}Far Mohamad}",

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T1 - Cnoidal Waves, Solitary Waves, Shock Waves and Conservation Laws of the Generalized Cubic Boussinesq-Type Model for Shallow Water Wave Dynamics

AU - Biswas, Anjan

AU - Wang, Ming Yue

AU - Kara, Abdul H.

AU - Yildirim, Yakup

AU - Moraru, Luminita

AU - Balanica, Carmelia M.

AU - Hussein, Layth

AU - Jawad, Anwar Ja’Far Mohamad

PY - 2025

Y1 - 2025

N2 - The paper addresses the latest form of Boussinesq equation with generalized form of cubic nonlinearity. The solitary waves are recovered from the model using traveling wave hypothesis. The conservation laws are recovered from the model. The conservation laws are obtained using the method of multipliers. Finally, the complete discriminant method yields shock waves and cnoidal waves as well. The numerical simulations supplement the analytical results.

AB - The paper addresses the latest form of Boussinesq equation with generalized form of cubic nonlinearity. The solitary waves are recovered from the model using traveling wave hypothesis. The conservation laws are recovered from the model. The conservation laws are obtained using the method of multipliers. Finally, the complete discriminant method yields shock waves and cnoidal waves as well. The numerical simulations supplement the analytical results.

KW - Boussinesq

KW - conservation laws

KW - shallow water

KW - solitary waves

UR - http://www.scopus.com/inward/record.url?scp=105001153859&partnerID=8YFLogxK

U2 - 10.37256/cm.6220256389

DO - 10.37256/cm.6220256389

M3 - Article

AN - SCOPUS:105001153859

SN - 2705-1064

VL - 6

SP - 1973

EP - 1987

JO - Contemporary Mathematics (Singapore)

JF - Contemporary Mathematics (Singapore)

IS - 2

ER -

Cnoidal Waves, Solitary Waves, Shock Waves and Conservation Laws of the Generalized Cubic Boussinesq-Type Model for Shallow Water Wave Dynamics

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Keywords

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