### Abstract

We derive an exact system of nonlinear equations that describe the dynamics of a degenerateHe

^{3}- He^{4}solution, and compute the nonlinear correction to the propagation velocity of first sound (proportional to the amplitude) in the collisionless limit. Our nonlinear treatment requires the third functional derivative of the total energy with respect to the distribution function of He^{3}quasi particles in addition to the second functional derivative (the Landau function). We find the Fermi-liquid parameters in the limit of small He^{3}concentrations from a microscopic calculation, and obtain an explicit expression for the correction.Original language | English |
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Pages (from-to) | 885-894 |

Number of pages | 10 |

Journal | Journal of Experimental and Theoretical Physics |

Volume | 82 |

Issue number | 5 |

Publication status | Published - 1996 |

Externally published | Yes |

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## Cite this

Andreev, A. F., Bazalii, Y. B., & Shevchenko, P. V. (1996). Nonlinear oscillations of a degenerate He

^{3}-He^{4}solution.*Journal of Experimental and Theoretical Physics*,*82*(5), 885-894.