Akhtar Hussain
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View article: Group Analysis of a Class of Nonlinear Wave Equations
Group Analysis of a Class of Nonlinear Wave Equations Open
We study the nature of a (2+1)-dimensional nonlinear wave equation using the Lie symmetry analysis method. This problem is reduced to ordinary differential equations (ODEs) using non-similar subalgebras of Lie symmetries. We presented expl…
View article: How do financial development and institutional quality influence greenhouse gases in the Next-11 economies?
How do financial development and institutional quality influence greenhouse gases in the Next-11 economies? Open
The sustainable development goals of many nations are challenged by the need to reduce emissions, improve ecological integrity, and address the impacts on climatic alteration. The study examines how the financial innovation and institution…
View article: Novel analytical solutions to the ( 3 + 1 ) -dimensional heat model using Lie symmetry method
Novel analytical solutions to the ( 3 + 1 ) -dimensional heat model using Lie symmetry method Open
View article: Sub pico-second pulses in mono-mode optical fibers with Triki-Biswas model
Sub pico-second pulses in mono-mode optical fibers with Triki-Biswas model Open
This study explores the Triki-Biswas (TB) model, a novel model describing soliton dynamics in monomodal optical fibers with non-Kerr dispersion, to obtain optical solitons. Optical bright and singular solitons were derived using the genera…
View article: Solitary and soliton solutions of the nonlinear fractional Chen Lee Liu model with beta derivative
Solitary and soliton solutions of the nonlinear fractional Chen Lee Liu model with beta derivative Open
The nonlinear Chen-Lee-Liu (NCLL) model is a crucial mathematical model for assessing optical fiber communication systems. It incorporates various factors, including noise, dispersion, and nonlinearity, which can influence signal quality a…
View article: Unraveling Symmetry Properties in a Three-Dimensional Nonlinear Evolution Model via the Lie Group Method
Unraveling Symmetry Properties in a Three-Dimensional Nonlinear Evolution Model via the Lie Group Method Open
This research focuses on a (3+1)-dimensional nonlinear evolution model originating from the Jaulent-Miodek hierarchy. Several tools can be used to examine the symmetry of the model. However, our primary emphasis lies in harnessing one of t…
View article: On the classification of group invariant solutions of the Barenblatt–Gilman model by a one-dimensional system of subalgebras
On the classification of group invariant solutions of the Barenblatt–Gilman model by a one-dimensional system of subalgebras Open
The Barenblatt–Gilman (BG) equation, which simulates nonequilibrium countercurrent capillary impregnation, is discussed in this study. By applying symmetry classification to the nonlinear function Φ(σ), six distinct cases emerge. In the ge…
View article: On the analysis and integrability of the time-fractional stochastic potential-KdV equation
On the analysis and integrability of the time-fractional stochastic potential-KdV equation Open
View article: Corrigendum to “Group theoretic approach to (4 + 1)-dimensional Boiti-Leon-Manna-Pempinelli equation” [Alex. Eng. J. 118 (2025) 449–465]
Corrigendum to “Group theoretic approach to (4 + 1)-dimensional Boiti-Leon-Manna-Pempinelli equation” [Alex. Eng. J. 118 (2025) 449–465] Open
View article: Invariant analysis and equivalence transformations for the non-linear wave equation in elasticity
Invariant analysis and equivalence transformations for the non-linear wave equation in elasticity Open
The phenomenon of elastic wave propagation within an inelastic material results in nonlinear wave equations. Our study specifically examines a unidirectional nonlinear elastic wave, incorporating considerations of a sixth-order Murnaghan p…
View article: Group theoretic approach to (4+1)-dimensional Boiti–Leon–Manna–Pempinelli equation
Group theoretic approach to (4+1)-dimensional Boiti–Leon–Manna–Pempinelli equation Open
This study introduces a novel integrable nonlinear evolution equation within 4+1 dimensions. This equation extends the well-established Boiti–Leon–Manna–Pempinelli (BLMP) Pempinelli equation. To delve into the integrability characteristics…
View article: Noether and partial Noether approach for the nonlinear (3+1)-dimensional elastic wave equations
Noether and partial Noether approach for the nonlinear (3+1)-dimensional elastic wave equations Open
The Lie group method is a powerful technique for obtaining analytical solutions for various nonlinear differential equations. This study aimed to explore the behavior of nonlinear elastic wave equations and their underlying physical proper…
View article: Novel Soliton and Wave Solutions for the Dual‐Perturbed Integrable Boussinesq Equation
Novel Soliton and Wave Solutions for the Dual‐Perturbed Integrable Boussinesq Equation Open
Nonlinear science represents a foundational frontier in scientific inquiry that explores the shared characteristics inherent in nonlinear phenomena. This study focused on the perturbed Boussinesq (PB) equation incorporating dual perturbati…
View article: Lie group analysis and its invariants for the class of multidimensional nonlinear wave equations
Lie group analysis and its invariants for the class of multidimensional nonlinear wave equations Open
We systematically classify Lie symmetries of a class of (2 + 1)-dimensional nonlinear wave equations. Our methodology proposes a symmetry classification for Lie generators applicable to four distinct cases inherent within this equation. Fo…
View article: Lie symmetry analysis, traveling wave solutions and conservation laws of a Zabolotskaya-Khokholov dynamical model in plasma physics
Lie symmetry analysis, traveling wave solutions and conservation laws of a Zabolotskaya-Khokholov dynamical model in plasma physics Open
This article analyzes the analytic and solitary wave solutions of the one-dimensional Zabolotskaya-Khokholov (ZK) dynamical model which provides information about the propagation of sound beam or confined wave beam in nonlinear media and s…
View article: Review of: "Bridging Classical and Computational Physics: Integrating Unsolvable Differential Equations into Undergraduate Education"
Review of: "Bridging Classical and Computational Physics: Integrating Unsolvable Differential Equations into Undergraduate Education" Open
View article: Diverse variety of exact solutions for some nonlinear models via the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.svg" display="inline" id="d1e602"><mml:mrow><mml:mo>(</mml:mo><mml:mfrac><mml:mrow><mml:msup><mml:mrow><mml:mi>G</mml:mi></mml:mrow><mml:mrow><mml:mo>′</mml:mo></mml:mrow></mml:msup></mml:mrow><mml:mrow><mml:mi>G</mml:mi></mml:mrow></mml:mfrac><mml:mo>)</mml:mo></mml:mrow></mml:math>-expansion method
Diverse variety of exact solutions for some nonlinear models via the -expansion method Open
In this article, we explore several significant nonlinear physical models, including the Benjamin–Bona–Mahony–Peregrine–Burgers (BBMPB) equation, the Burgers–Korteweg–De Vries (BK) equation, the one-dimensional Oskolkov (OSK) equation, the…
View article: Analyzing invariants and employing successive reductions for the extended Kadomtsev Petviashvili equation in (3+1) dimensions
Analyzing invariants and employing successive reductions for the extended Kadomtsev Petviashvili equation in (3+1) dimensions Open
In this research, we employ the potent technique of Lie group analysis to derive analytical solutions for the (3+1)-extended Kadomtsev-Petviashvili (3D-EKP) equation. The systematic application of this method enables the identification of …
View article: Exact solutions for the Cahn–Hilliard equation in terms of Weierstrass-elliptic and Jacobi-elliptic functions
Exact solutions for the Cahn–Hilliard equation in terms of Weierstrass-elliptic and Jacobi-elliptic functions Open
View article: Dispersive modified Benjamin-Bona-Mahony and Kudryashov-Sinelshchikov equations: non-topological, topological, and rogue wave solitons
Dispersive modified Benjamin-Bona-Mahony and Kudryashov-Sinelshchikov equations: non-topological, topological, and rogue wave solitons Open
This study delves into the exploration of three distinct envelope solitons within the nonlinear dispersive modified Benjamin Bona Mahony (NDMBBM) equation, originating from seismic sea waves, and the Kudryashov-Sinelshchikov (KS) equation.…
View article: Dynamics of invariant solutions of the DNA model using Lie symmetry approach
Dynamics of invariant solutions of the DNA model using Lie symmetry approach Open
View article: Dynamic nature of analytical soliton solutions of the nonlinear ZKBBM and GZKBBM equations
Dynamic nature of analytical soliton solutions of the nonlinear ZKBBM and GZKBBM equations Open
A solitary wave, characterized as a localized perturbation in a medium, emerges as a result of a delicate equilibrium between nonlinear and dispersive phenomena. Solitons, a subtype of solitary waves, exhibit persistent shape and velocity …
View article: Some New Families of Exact Solitary Wave Solutions for Pseudo-Parabolic Type Nonlinear Models
Some New Families of Exact Solitary Wave Solutions for Pseudo-Parabolic Type Nonlinear Models Open
The objective of the current study is to provide a variety of families of soliton solutions to pseudo-parabolic equations that arise in nonsteady flows, hydrostatics, and seepage of fluid through fissured material. We investigate a class o…
View article: Optimal system, invariant solutions and dynamics of the solitons for the Wazwaz Benjamin Bona Mahony equation
Optimal system, invariant solutions and dynamics of the solitons for the Wazwaz Benjamin Bona Mahony equation Open
In this article, the nonlinear (3+1) dimensional Wazwaz Benjamin Bona Mahony (WBBM) equation is considered for analysis which is related to some specific undular bore evolution through a long wave in shallow water. One-dimensional optimal …
View article: Invariance properties of the microstrain wave equation arising in microstructured solids
Invariance properties of the microstrain wave equation arising in microstructured solids Open
The Lie group method stands as a significant, powerful, and straightforward mathematical tool for discovering precise invariant solutions and traveling wave solutions in prevalent nonlinear evolution equations across engineering, applied m…
View article: Invariance and Ibragimov approach with Lie algebra of a nonlinear coupled elastic wave system
Invariance and Ibragimov approach with Lie algebra of a nonlinear coupled elastic wave system Open
The propagation of elastic waves in hyperelastic materials is described by a nonlinear system of partial differential equations (PDEs) governing the material’s motion. Hyperelastic materials are characterized by a strain–energy density fun…
View article: Symmetry analysis and invariant solutions of generalized coupled Zakharov-Kuznetsov equations using optimal system of Lie subalgebra
Symmetry analysis and invariant solutions of generalized coupled Zakharov-Kuznetsov equations using optimal system of Lie subalgebra Open
This research focuses on the examination of nonlinear evolution equations, with a specific emphasis on the generalized coupled Zakharov-Kuznetsov (CZK) equations serving as a primary application. Given the wide application of classical Lie…
View article: Dynamical behavior of solitons of the (2+1)-dimensional Konopelchenko Dubrovsky system
Dynamical behavior of solitons of the (2+1)-dimensional Konopelchenko Dubrovsky system Open
View article: Invariant Analysis of the Time-Fractional Potential Kdv Equation
Invariant Analysis of the Time-Fractional Potential Kdv Equation Open
View article: A discussion on the Lie symmetry analysis, travelling wave solutions and conservation laws of new generalized stochastic potential-KdV equation
A discussion on the Lie symmetry analysis, travelling wave solutions and conservation laws of new generalized stochastic potential-KdV equation Open
In this current study, the potential-KdV equation has been altered by the addition of a new stochastic term. The transmission of nonlinear optical solitons and photons is described by the new stochastic potential-KdV (spKdV), which applies…