一类四阶线性微分算子散射数据的时间演化
Time evolution of the scattering data for a fourth-order linear differential operator
摘要：
得到了微分算子$\displaystyle\frac{d^4}{dx^4} +\displaystyle\frac{d}{dx} u(x,t)\displaystyle\frac{d}{dx}+v(x,t),$的散射和光谱数据的时间演化，其中$u(x,t)$和$v(x,t)$是在每个固定的$t.$上按$x\to\pm\infty$指数衰减的实值势。该结果与逆散射变换方法的关键步骤有关，该方法用于求解由$u(x,t)$和$v(x,t).$满足的一对耦合非线性偏微分方程的初值问题
英文摘要：
The time evolution of the scattering and spectral data is obtained for the differential operator $\displaystyle\frac{d^4}{dx^4} +\displaystyle\frac{d}{dx} u(x,t)\displaystyle\frac{d}{dx}+v(x,t),$ where $u(x,t)$ and $v(x,t)$ are real-valued potentials decaying exponentially as $x\to\pm\infty$ at each fixed $t.$ The result is relevant in a crucial step of the inverse scattering transform method that is used in solving the initial-value problem for a pair of coupled nonlinear partial differential equations satisfied by $u(x,t)$ and $v(x,t).$
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