Construction of travelling wave solutions of coupled Higgs equation and the Maccari system via two analytical approaches

Yousaf, Muhammad Zain; Abbas, Muhammad; Abdullah, Farah Aini; Nazir, Tahir; Alzaidi, Ahmed SM.; Emadifar, Homan

doi:10.1007/s11082-024-06708-w

Opt Quant Electron

2024

DOI: 10.1007/s11082-024-06708-w

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Construction of travelling wave solutions of coupled Higgs equation and the Maccari system via two analytical approaches

Muhammad Zain Yousaf,

Muhammad Abbas,

Farah Aini Abdullah

et al.

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2024

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Cited by 3 publications

References 46 publications

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Abundant different types of soliton solutions with stability analysis for the $$(2 + 1)$$-dimensional extended shallow water wave equation in ocean engineering with applications

Yousaf,

Abbas,

Iqbal

et al. 2024

Nonlinear Dyn

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Abundant different types of soliton solutions with stability analysis for the $$(2 + 1)$$-dimensional extended shallow water wave equation in ocean engineering with applications

Yousaf,

Abbas,

Iqbal

et al. 2024

Nonlinear Dyn

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Adequate dynamical perspective of traveling wave solutions to the perturbed Boussinesq equation appearing in ocean engineering

Yousaf,

Abbas,

Iqbal

et al. 2024

J. Ocean Eng. Mar. Energy

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Abundant Soliton Solutions to the Generalized Reaction Duffing Model and Their Applications

Vivas-Cortez,

Aftab,

Abbas

et al. 2024

Symmetry

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The main aim of this study is to obtain soliton solutions of the generalized reaction Duffing model, which is a generalization for a collection of prominent models describing various key phenomena in science and engineering. The equation models the motion of a damped oscillator with a more complex potential than in basic harmonic motion. Two effective techniques, the mapping method and Bernoulli sub-ODE technique, are used for the first time to obtain the soliton solutions of the proposed model. Initially, the traveling wave transform, which comes from Lie symmetry infinitesimals, is applied, and a nonlinear ordinary differential equation form is derived. These approaches effectively retrieve a hyperbolic, Jacobi function as well as trigonometric solutions while the appropriate conditions are applied to the parameters. Numerous innovative solutions, including the kink wave, anti-kink wave, bell shape, anti-bell shape, W-shape, bright, dark and singular shape soliton solutions, were produced via the mapping and Bernoulli sub-ODE approaches. The research includes comprehensive 2D and 3D graphical representations of the solutions, facilitating a better understanding of their physical attributes and proving the effectiveness of the proposed methods in solving complex nonlinear equations. It is important to note that the proposed methods are competent, credible and interesting analytical tools for solving nonlinear partial differential equations.

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Construction of travelling wave solutions of coupled Higgs equation and the Maccari system via two analytical approaches

Cited by 3 publications

References 46 publications

Abundant different types of soliton solutions with stability analysis for the $$(2 + 1)$$-dimensional extended shallow water wave equation in ocean engineering with applications

Abundant different types of soliton solutions with stability analysis for the $$(2 + 1)$$-dimensional extended shallow water wave equation in ocean engineering with applications

Adequate dynamical perspective of traveling wave solutions to the perturbed Boussinesq equation appearing in ocean engineering

Abundant Soliton Solutions to the Generalized Reaction Duffing Model and Their Applications

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