Modulation for Nonlinear Wave in Dissipative or Unstable Media

概要

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Modulation of an nonlinear wave in a dissipative and dispersive medium is considered by the method of multiple scales. The slow variables for the amplitude are determined by the coupling between the nonlinearity of the envelope wave and the dissipative or dispersive effect. A perturbation theory is developed for a system of equations which, when linearized, has a plane wave solution with complex frequency of a small imaginary part. Governing equation for the amplitude becomes a type of generalized nonlinear Schrodinger equation in three dimensions. For spatially periodic case, there may be the case that small dissipation can make the wave grow depending on the initial amplitude. As an illustrative example of the general theory, modulation of the convective mode in a fluid layer heated from below is considered.
社団法人日本物理学会の論文
1974-03-15