Analytical and Convergent LADM Solutions of Extended (3+1)-Dimensional Kairat–II and Kairat–X Equations

Hami Gündoğdu

doi:10.26650/ijmath.2026.00033

Analytical and Convergent LADM Solutions of Extended (3+1)-Dimensional Kairat–II and Kairat–X Equations

Abstract

This study explores the dynamics of the extended (3+1)-dimensional Kairat–II and Kairat–X equations, which represent advanced higher-dimensional generalizations incorporating linear dispersion and mixed-derivative terms. By constructing explicit lump-type exact solutions, we establish a robust foundation for formulating well-posed initial value problems. These analytical benchmarks serve as the basis for developing high-order Laplace–Adomian Decomposition Method (LADM) expansions, accompanied by a stringent analysis of their convergence and error metrics. Numerical simulations confirm that the truncated LADM series converge swiftly to the exact results, maintaining exceptional accuracy across representative parameter regimes. By bridging the gap between exact analytical solutions and high-efficiency numerical approximations, this work provides a comprehensive framework for addressing the computational challenges inherent in high-dimensional nonlinear partial differential equations.

Keywords

References

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Details

Primary Language

English

Subjects

Pure Mathematics (Other)

Journal Section

Research Article

Authors

Hami Gündoğdu ^*
0000-0002-7042-1885
Türkiye

Publication Date

June 30, 2026

Submission Date

November 26, 2025

Acceptance Date

April 21, 2026

Published in Issue

Year 2026 Volume: 4 Number: 1

DOI

https://doi.org/10.26650/ijmath.2026.00033

IZ

https://izlik.org/JA82HZ65RY

Cite

RIS / Bibtex

APA

Gündoğdu, H. (2026). Analytical and Convergent LADM Solutions of Extended (3+1)-Dimensional Kairat–II and Kairat–X Equations. Istanbul Journal of Mathematics, 4(1), 23-30. https://doi.org/10.26650/ijmath.2026.00033

AMA

1.Gündoğdu H. Analytical and Convergent LADM Solutions of Extended (3+1)-Dimensional Kairat–II and Kairat–X Equations. Istanbul Journal of Mathematics. 2026;4(1):23-30. doi:10.26650/ijmath.2026.00033

Chicago

Gündoğdu, Hami. 2026. “Analytical and Convergent LADM Solutions of Extended (3+1)-Dimensional Kairat–II and Kairat–X Equations”. Istanbul Journal of Mathematics 4 (1): 23-30. https://doi.org/10.26650/ijmath.2026.00033.

EndNote

Gündoğdu H (June 1, 2026) Analytical and Convergent LADM Solutions of Extended (3+1)-Dimensional Kairat–II and Kairat–X Equations. Istanbul Journal of Mathematics 4 1 23–30.

IEEE

[1]H. Gündoğdu, “Analytical and Convergent LADM Solutions of Extended (3+1)-Dimensional Kairat–II and Kairat–X Equations”, Istanbul Journal of Mathematics, vol. 4, no. 1, pp. 23–30, June 2026, doi: 10.26650/ijmath.2026.00033.

ISNAD

Gündoğdu, Hami. “Analytical and Convergent LADM Solutions of Extended (3+1)-Dimensional Kairat–II and Kairat–X Equations”. Istanbul Journal of Mathematics 4/1 (June 1, 2026): 23-30. https://doi.org/10.26650/ijmath.2026.00033.

JAMA

1.Gündoğdu H. Analytical and Convergent LADM Solutions of Extended (3+1)-Dimensional Kairat–II and Kairat–X Equations. Istanbul Journal of Mathematics. 2026;4:23–30.

MLA

Gündoğdu, Hami. “Analytical and Convergent LADM Solutions of Extended (3+1)-Dimensional Kairat–II and Kairat–X Equations”. Istanbul Journal of Mathematics, vol. 4, no. 1, June 2026, pp. 23-30, doi:10.26650/ijmath.2026.00033.

Vancouver

1.Hami Gündoğdu. Analytical and Convergent LADM Solutions of Extended (3+1)-Dimensional Kairat–II and Kairat–X Equations. Istanbul Journal of Mathematics. 2026 Jun. 1;4(1):23-30. doi:10.26650/ijmath.2026.00033