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  "body": "\n## Summary\n\nA rarefaction wave is a continuous solution of a [[conservation law|8RA7AMWSAF]] that spreads out from a point like a fan.\nIn the fan, the unknown takes every value between two states.\nIt is self-similar: it depends only on $x/t$.\nIt is the admissible solution when the characteristics on the two sides of a jump move apart.\nIn that case a [[shock wave|JSDMGGTG7G]] would violate the entropy condition.\nTogether with shocks and contact discontinuities, rarefaction waves are the building blocks of solutions of the [[Riemann problem|GJWKX22VVE]].\nSee the [[definition|MM6TXKN90V]].\n\n## Explanations\n\n### L1 human\n\nWhen a traffic light turns green, the dense queue of cars does not leave as one block.\nThe front cars drive off fast, the cars behind start later, and the queue thins out gradually.\nThe density goes smoothly from jammed to free over a stretch of road that grows with time.\nThis spreading fan is a rarefaction wave.\nFor Burgers' equation with value $0$ on the left and $1$ on the right, it is $u(x, t) = x/t$ for $0 \\le x \\le t$.\n",
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