一维半线性双曲系统解的整体存在性和驻波解

Global existence of one-dimensional semilinear hyperbolic systems and standing wave solution

研究了一维空间中的半线性双曲系统初值问题的一类具有特殊形式的解.当方程∂_(t)U+∂_(x)U+mV=-αUV∂_(t)V-∂_(x)V-mU=βU^(2)的常数α=β时,利用先验估计得到了方程的解具有整体存在性,同时通过求解常微分方程得到了方程的驻波解.另外,对方程的通解进行了讨论.

A kind of solutions with special form for the initial value problem of semilinear hyperbolic system in one dimensional space are studied.When the constant of equation∂_(t)U+∂_(x)U+mV=-αUV∂_(t)V-∂_(x)V-mU=βU^(2) satisfiesα=β,the global existence of the solution of equation is obtained by using a priori estimation,and the standing wave solution of equation is obtained by solving the ordinary differential equation.In addition,the general solution of equation is discussed.