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Dergiler / Istanbul Journal of Mathematics / 2026 / Volume: 4 Issue: 1

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

Hami Gündoğdu(SAKARYA UNIVERSITY)0000-0002-7042-1885
Sayfa
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Yayın Tarihi
2026-06-30
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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.

📌 3 Maddede Bu Makale

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Amaç & Hipotez: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.
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Temel Bulgular & Veri:By constructing explicit lump-type exact solutions, we establish a robust foundation for formulating well-posed initial value problems.
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Sonuç & Katkı: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.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Approximate analytical solution · Error analysis · Kairat–II equation

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.

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Bu Makaleye Atıf Yap

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

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