Symmetry analysis, optimal subalgebra, quasi-self-adjointness condition with conservation laws and analytical solutions for the ($$1+1$$)-dimensional Pochhammer–Chree model in longitudinal wave propagation

Vinita,; Saha Ray, S

doi:10.1007/s12043-023-02722-x

Pramana - J Phys

2024

DOI: 10.1007/s12043-023-02722-x

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Symmetry analysis, optimal subalgebra, quasi-self-adjointness condition with conservation laws and analytical solutions for the ($$1+1$$)-dimensional Pochhammer–Chree model in longitudinal wave propagation

Vinita,

S Saha Ray

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Cited by 2 publications

References 31 publications

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High accuracy solutions for the Pochhammer–Chree equation in elastic media

Khater,

Alfalqi

2024

Sci Rep

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This study investigates the nonlinear Pochhammer–Chree equation, a model crucial for understanding wave propagation in elastic rods, through the application of the Khater III method. The research aims to derive precise analytical solutions and validate them using He’s variational iteration method (VIM). The Pochhammer–Chree equation’s relationship to other nonlinear evolution equations, such as the Korteweg-de Vries and nonlinear Schrödinger equations, underscores its significance in the field of nonlinear wave dynamics. The methodology employs the Khater III method for deriving analytical solutions, while He’s VIM serves as a numerical validation tool, ensuring the accuracy and stability of the obtained results. This dual approach not only yields novel solutions but also provides a robust framework for analyzing complex wave phenomena in elastic media. The findings of this study have significant implications for material science and engineering applications, offering new insights into the behavior of waves in elastic rods. By bridging the gap between theoretical models and practical applications, this research contributes to the advancement of both mathematical theory and physical understanding of nonlinear wave dynamics. Situated within the domain of applied mathematics, with a focus on nonlinear wave equations, this work exemplifies the interdisciplinary nature of contemporary research in mathematical physics. The results presented herein open new avenues for future investigations in related fields and highlight the potential for innovative applications in material science and engineering.

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High accuracy solutions for the Pochhammer–Chree equation in elastic media

Khater,

Alfalqi

2024

Sci Rep

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Nonlinear effects in quantum field theory: Applications of the Pochhammer–Chree equation

Khater

2024

Mod. Phys. Lett. B

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This study aims to solve the nonlinear Pochhammer–Chree ([Formula: see text]) equation to understand its physical implications and establish connections with other nonlinear evolution equations, particularly in plasma dynamics. By using the Khater II ([Formula: see text]hat. II) method for analytical solutions and validating these solutions numerically with the variational iteration method, this study offers a detailed understanding of the equation’s behavior. The results demonstrate the effectiveness of these methods in accurately modeling the system, highlighting the importance of combining analytical and numerical approaches for reliable solutions. This research significantly advances the field of nonlinear dynamics, especially in plasma physics, by employing multidisciplinary methods to tackle complex physical processes. Moreover, the [Formula: see text] equation is relevant in various physical contexts beyond plasma dynamics such as optical and quantum fields. In optics, it models the propagation of nonlinear waves in fiber optics, where similar nonlinear evolution equations describe wave interactions. In quantum field theory, the [Formula: see text] equation helps in understanding the behavior of quantum particles and fields under nonlinear effects, making it a versatile tool for studying complex phenomena across different domains of physics.

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Symmetry analysis, optimal subalgebra, quasi-self-adjointness condition with conservation laws and analytical solutions for the ($$1+1$$)-dimensional Pochhammer–Chree model in longitudinal wave propagation

Cited by 2 publications

References 31 publications

High accuracy solutions for the Pochhammer–Chree equation in elastic media

High accuracy solutions for the Pochhammer–Chree equation in elastic media

Nonlinear effects in quantum field theory: Applications of the Pochhammer–Chree equation

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