A comprehensive study of numerical and analytical approaches to the q -deformed equation

Research in Mathematics, Journal Year: 2025, Volume and Issue: 12(1)

Published: Jan. 17, 2025

This research provides a comprehensive investigation of the q-deformed Tanh-Gordon model. Because it sheds light on how physical systems behave, this model is especially helpful when researching with violated symmetries. For certain parameter values, (H+G′G2)-expansion method used to solve equation. produces analytical solutions that provide important insights into dynamics and behavior system. These increase our grasp system's features underlying mathematics. The equation also numerically solved using finite difference approach confirm accuracy solutions. numerical improves dependability results guarantees To facilitate understanding comparison, paper includes tables visuals. By enhancing data's readability clarity, these illustrations help readers recognize parallels discrepancies between

Language: Английский

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Application of the residual power series method to find optical soliton solutions for the (3+1) q-deformed tanh-Gordon equation

Zeitschrift für angewandte Mathematik und Physik, Journal Year: 2025, Volume and Issue: 76(3)

Published: May 3, 2025

Language: Английский

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Investigating novel optical soliton solutions for a generalized (3+1)-dimensional q-deformed equation

Zeitschrift für angewandte Mathematik und Physik, Journal Year: 2024, Volume and Issue: 75(6)

Published: Oct. 26, 2024

Abstract In this study, we investigate the (3+1) q -deformed tanh-Gordon equation due to its importance in context of mathematical physics. It describes solitonic solutions quantum field theory; it can sometimes be used condensed matter physics describe interactions between particles magnetic materials or superconductors; model light propagation nonlinear optical fibers photonic crystals where refractive index has a structure; and also applied studying shock waves, turbulence rogue waves deformation introduces corrections classical wave phenomena. Utilizing $$(\frac{{\mathfrak {G}}^{\prime }}{\omega {\mathfrak }+{\mathfrak {G}}+r})$$ ( G ′ ω + r ) -expansion technique, derive novel analytical that enhance our understanding underlying dynamics. Additionally, employ finite element method (extended cubic B-spline method) validate findings explore behavior under different parameter regimes. Our results demonstrate versatility framework generating rich phenomena, paving way for future research both theoretical

Language: Английский

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Fractional analysis of the (2+1) $$\mathfrak {q}$$-deformed tanh-Gordon equation with optimal homotopy with $$\mathbb {J}$$-transform

Zeitschrift für angewandte Mathematik und Physik, Journal Year: 2024, Volume and Issue: 75(6)

Published: Nov. 21, 2024

Language: Английский

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