The Existence And Properties Of The Kernel Sections For The Dissipative Modified Zakharov Equations

Dynamical system is an important part of nonlinear science, it studies the global qualitative behavior of the system with time evolution. This thesis studies the dynamical behaviors of the non-autonomous lattice dissipative modified Zakharov equations. It is organized as follows.The first chapter is introduction. Firstly, it briefly introduces the origin of the infinite dimensional dynamical system and lattice system, then it displays the issues addressed in this thesis.In chapter 2, it firstly proves the existence of kernel sections for the process generated by the solution operators of the dissipative modified Zakharov equations and then give an upper bound of the Kolmogorov e-entropy for the kernel sections; Secondly, it obtains an upper bound of fractal dimension of the kernel sections, Finally, it verifies the upper semicontinuity of the kernel sections.In chapter 3, it summarizes the thesis briefly.