内蒙古民族大学学报（自然科学版）2026，Vol.41Issue(2)：76-83,8.DOI:10.14045/j.cnki.15-1220.2026.02.010
ill-posed Boussinesq方程的守恒律及其解的构造
Conservation Laws of ill-posed Boussinesq Equation and Construction of Their Solutions
摘要
Abstract
The construction of conservation laws,numerical simulation of traveling wave solutions,and the deriva-tion of Lump-Kink solutions for the ill-posed Boussinesq equation were studied.Initially,he conservation laws for this equation are constructed using the Symmetry/adjoint symmetry pair method,the recurrence formula method,and the multiplier method respectively,and the obtained results were compared and analyzed.Subsequently,the variational it-eration method was applied to numerically simulate the traveling wave solution of the equation.Finally,the Lump-Kink solutions of the equation were derived via the Hirota bilinear method.The research indicates that the conservation laws of this equation constructed by the three methods are entirely consistent,the variational iteration method can simulate the traveling wave solutions of this equation with high accuracy,and the Hirota method can precisely yield the explicit forms of the Lump-Kink solutions of this equation.关键词
ill-posed Boussinesq方程/对称-共轭对称'对'方法/变分迭代法/Hirota双线性方法/守恒律Key words
ill-posed Boussinesq equation/Symmetry/adjoint symmetry pair method/variational iteration method/Hirota bilinear method/conservation law分类
数理科学引用本文复制引用
刘亚峰,额尔敦布和,刘欣..ill-posed Boussinesq方程的守恒律及其解的构造[J].内蒙古民族大学学报（自然科学版）,2026,41(2):76-83,8.基金项目
内蒙古自治区直属高校基本科研业务费项目(ZSLJ202203) （ZSLJ202203）
