ill-posed Boussinesq方程的守恒律及其解的构造OA

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.