Bifurcation, bilinear forms, conservation laws and soliton solutions of the temporal-second-order KdV equation

Ahmed, Engy A.; Wael, Shrouk; Seadawy, Aly R.; Maowad, S.M.; El-Kalaawy, Omar H.

doi:10.1142/s0217979222501818

Cited by 2 publications

(1 citation statement)

References 47 publications

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“…In Ref. [26], the bell polynomial method was proved to be a powerful mathematical tool for solving the KdV equation with variable coefficients to reach the N-soliton solutions. Additionally, the periodic wave solutions were obtained by using the Riemann function method.…”

Section: Introductionmentioning

confidence: 99%

Exact Solutions for Coupled Variable Coefficient KdV Equation via Quadratic Jacobi’s Elliptic Function Expansion

Zeng

Liang

et al. 2023

Symmetry

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The exact traveling wave solutions to coupled KdV equations with variable coefficients are obtained via the use of quadratic Jacobi’s elliptic function expansion. The presented coupled KdV equations have a more general form than those studied in the literature. Nine couples of quadratic Jacobi’s elliptic function solutions are found. Each couple of traveling wave solutions is symmetric in mathematical form. In the limit cases m→1, these periodic solutions degenerate as the corresponding soliton solutions. After the simple parameter substitution, the trigonometric function solutions are also obtained.

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Section: Introductionmentioning

confidence: 99%

Exact Solutions for Coupled Variable Coefficient KdV Equation via Quadratic Jacobi’s Elliptic Function Expansion

Zeng

Liang

et al. 2023

Symmetry

View full text Add to dashboard Cite

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Analysis of optical solitons propagation in the dual-mode resonant nonlinear Schrödinger dynamical equation with assorted nonlinear interactions

Rehman,

Khushi,

Iqbal

et al. 2024

Mod. Phys. Lett. B

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This research explores the dual-mode manifestation within the nonlinear Schrödinger equation, elucidating the amplification or absorption of paired waves. This study delves into the simultaneous generation of two distinct waves associated with the dual-mode phenomenon with three crucial parameters: phase velocity, nonlinearity and dispersive factor. The resulting wave phenomena from these solutions have implications across various fields, including fluid dynamics, water wave mechanics, ocean engineering and scientific inquiry. The study employs the modified Sardar sub-equation method to obtain the optical soliton solutions, encompassing various types such as dark, bright, singular, combo dark–singular, periodic singular and dark–bright solitons. The obtained results highlight the reliability and simplicity of the modified Sardar sub-equation method. Additionally, the paper delves into the parametric conditions crucial for shaping and sustaining these solitons. The research explores the interaction of dual waves and the variation in wave speed. Furthermore, dynamic phenomena are illustrated, and the physical implications of the solutions are interpreted using 3D and 2D plots with different parameter values.

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Bifurcation, bilinear forms, conservation laws and soliton solutions of the temporal-second-order KdV equation

Cited by 2 publications

References 47 publications

Exact Solutions for Coupled Variable Coefficient KdV Equation via Quadratic Jacobi’s Elliptic Function Expansion

Exact Solutions for Coupled Variable Coefficient KdV Equation via Quadratic Jacobi’s Elliptic Function Expansion

Analysis of optical solitons propagation in the dual-mode resonant nonlinear Schrödinger dynamical equation with assorted nonlinear interactions

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