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Quasiperiodic waves and asymptotic behavior for the nonisospectral and variable-coefficient KdV equation

机译：非异构体和可变系数KDV方程的QuaSipheriodic波和渐近行为

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摘要

In this paper, quasiperiodic waves and asymptotic behavior for the nonisospectral and variable-coefficient KdV (nvcKdV) equation are considered. The Hirota bilinear method is extended to explicitly construct multiperiodic (quasiperiodic) wave solutions for the nvcKdV equation. And a limiting procedure is presented to analyze asymptotic behavior of the one- and two-periodic waves in details. The exact relations between the periodic wave solutions and the well-known soliton solutions are established. It is rigorously shown that the periodic wave solutions tend to the soliton solutions under a small amplitude limit.
机译：在本文中，考虑了非分辨率和可变系数KDV（NVCKDV）方程的QuaSiodic波和渐近行为。 Hirota Bilinear方法扩展以明确构建NVCKDV方程的多体期（QuaSipheriodic）波解决方案。提出了一个限制程序，以分析细节中单周期波的渐近行为。建立了周期性波解决方案与众所周知的孤子解决方案之间的确切关系。它经过严格地示出了周期性波解倾向于在小幅度极限下的孤子溶液。

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