应用数学2026，Vol.39Issue(3)：867-879,13.
一种广义(3+1)维非线性发展方程的Lax可积性与精确解
Lax Integrability and Exact Solutions of a Generalized(3+1)-Dimensional Nonlinear Evolution Equation
摘要
Abstract
Based on the Bell polynomial method and the trial function method,we investigate the Lax integrability and exact solutions of a generalized(3+1)-dimensional nonlinear evolution equation.First,by employing the Bell polynomial method,we derive the bilinear form,bilinear Bäcklund transfor-mation,Lax pair,and infinite conservation laws of the equation.Second,based on the bilinear Bäcklund transformation,we establish the corresponding nonlinear superposition formula for the solutions.Fur-thermore,using the trial function method,we obtain a double solition solution by solving the nonlinear superposition formula.Finally,with the aid of the Mathematica symbolic computation system,we analyze the properties of the composite solutions by selecting appropriate parameters.关键词
Bell多项式法/双线性Bäcklund变换/无穷守恒律/解的非线性叠加公式/精确解Key words
Bell-polynomial method/Bilinear Bäcklund transformation/Infinite conservation law/Nonlinear superposition formula for solutions/Exact solution分类
数理科学引用本文复制引用
尹心怡,套格图桑..一种广义(3+1)维非线性发展方程的Lax可积性与精确解[J].应用数学,2026,39(3):867-879,13.基金项目
内蒙古自治区高校创新科研团队计划(NMGIRT2414) （NMGIRT2414）
内蒙古自治区自然科学基金资助项目(2024MS01003) （2024MS01003）
内蒙古自治区一流学科科研专项项目(YLXKZX-NSD-001 （）
YLXKZX-NSD-009) （）
内蒙古师范大学基本科研业务费专项资金资助项目(2022JBZD011) （2022JBZD011）
