论文标题
tzitzéica方程的逆散射变换
Inverse scattering transform for the Tzitzéica equation
论文作者
论文摘要
反向散射变换扩展以研究tzitzéica方程。引入了一组截面分析的特征和辅助本征。我们注意到，在此过程中，辅助本征起来起着重要作用。此外，讨论了分析本征函数和散射数据的对称性。 jost本征函数的渐近行为是系统地得出的。构建了一个Riemann-Hilbert问题来研究反散射问题。最后，获得了一些新颖的精确解决方案，以实现无反射电势。
The inverse scattering transform is extended to investigate the Tzitzéica equation. A set of sectionally analytic eigenfunctions and auxiliary eigenfunctions are introduced. We note that in this procedure, the auxiliary eigenfunctions play an important role. Besides, the symmetries of the analytic eigenfunctions and scattering data are discussed. The asymptotic behaviors of the Jost eigenfunctions are derived systematically. A Riemann-Hilbert problem is constructed to study the inverse scattering problem. Lastly, some novel exact solutions are obtained for reflectionless potentials.
