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arXiv · 0805.3554

Time evolution of the scattering data for a fourth-order linear differential operator

Tuncay Aktosun·Vassilis G. Papanicolaou
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Abstract

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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Tuncay Aktosun, Vassilis G. Papanicolaou. 2008-05-22. Time evolution of the scattering data for a fourth-order linear differential operator. https://doi.org/10.1088/0266-5611%2F24%2F5%2F055013

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