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

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.Mathematics Subject Classification (2020):35L05 35L70 35C10 65M70 65M99