Spacial Decay Properties Of A Two-component Integrable System With Peaked Soliton Solutions

This thesis is concerned with the spacial decay properties of a two-component integrable system with peaked soliton solutions and cubic nonlinearity.In the first chapter,we introduce the research backgrounds and contents.In the second chapter,we briefly introduce some preliminaries which will be used later on.In the third chapter,we first rewrite the system as its nonlocal weak form,and then study the spacial decay properties of the strong solutions to the Cauchy problem by using the energy method.More precisely,we prove that the corresponding strong solutions to the Cauchy problem for the model will decay exponentially and algebraically within its lifespan,whenever the initial data decay exponentially and algebraically,respectively.In the last chapter,we focus on the summary and some further problems of this research.