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Let the solution of the equation be \(u\left( {x,t} \right) = ae^{{i\left( {kx - \omega t} \right)}}\) . Substituting this into the given equation gives \(k - \omega = 0 \Rightarrow c_{0} = \frac{\omega }{k} = 1\) . It can be seen that the phase speed \({c}_{0}\) is constant and hence the solution to the given equation is a non-dispersive wave.

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Traveling Waves

  • 章节

  • 出版模式：

    开放获取

  • 发表日期：

    2025年

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  • Zeng He,
  • Wen Jiang,
  • Lin Wang

摘要

Let the solution of the equation be \(u\left( {x,t} \right) = ae^{{i\left( {kx - \omega t} \right)}}\) . Substituting this into the given equation gives \(k - \omega = 0 \Rightarrow c_{0} = \frac{\omega }{k} = 1\) . It can be seen that the phase speed \({c}_{0}\) is constant and hence the solution to the given equation is a non-dispersive wave.