Analysis of Instability of Solutions of Nonlinear Dissipative Equations

Abstract

In order to solve the difficult and unstable problems of solving nonlinear dissipation equations, this paper studies some important nonlinear dissipation equations and related problems in the soliton theory based on the idea of mathematical mechanization. This paper introduces the historical development and current status of the theory of solving nonlinear dissipation equations and its mathematical mechanization. Calculated the initial value problem of the nonlinear dissipation equation, analyzed the integrability and nonlinear eigenvalue problem of the nonlinear dissipation equation, solved the constructiveness of the nonlinear evolution equation system, and finally analyzed the instability of its solution . Through research, apply mathematical methods to related disciplines and become a good mathematical calculation tool for solving practical complex problems.