Dissipation mechanics and exact solutions for nonlinear equations of dissipative type—Principle and application of dissipation mechanics (I)

Abstract

This work is the continuation and the distillation of the discussion of Refs. [1-4]. (A) From complementarity principle we build up dissipation mechanics in this paper. It is a dissipative theory of correspondence with the quantum mechanics. From this theory we can unitedly handle problems of macroscopic non-equilibrium thermodynamics and viscous hydrodynamics, and handle each dissipative and irreversible problems in quantum mechanics. We prove the basic equations of dissipation mechanics to eigenvalues equations of correspondence with the Schrodinger equation or Dirac equation in this paper. (B) We unitedly merge the basic nonlinear equations of dissipative type, especially the Navier-Stokes equation as a basic equation for macroscopic non-equilibrium thermodynamics and viscous hydrodynamics into integrability condition of basic equation of dissipation mechanics. And we can obtain their exact solutions by the inverse scattering method in this paper.