Tzitzéica方程的逆散射变换
Inverse scattering transform for the Tzitzéica equation
摘要：
将逆散射变换推广到研究Tzitzéica方程。引入了一组分段解析的本征函数和辅助本征函数。我们注意到，在这个过程中，辅助本征函数起着重要的作用。此外，还讨论了解析本征函数和散射数据的对称性。系统地导出了Jost本征函数的渐近行为。构造了一个Riemann-Hilbert问题来研究逆散射问题。最后，得到了无反射势的一些新的精确解。
英文摘要：
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.
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