恰普雷金方程（英語：Chaplygin equation）是俄羅斯物理學家謝爾蓋·阿列克謝耶維奇·恰普雷金在1904年發表的描寫噴氣流的非線性偏微分方程：[1]
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解析解
![{\displaystyle u(x,t)=_{C}1+_{C}2*(_{C}3+C[1]*x+_{C}4*t)}](http://wikimedia.org/api/rest_v1/media/math/render/svg/c48e22509349f7de291cab4f3d4173f4af0ae76a)
![{\displaystyle u(x,t)=_{C}1+((1/2)*\pi -_{C}3-C[1]*x-_{C}4*t)*_{C}2}](http://wikimedia.org/api/rest_v1/media/math/render/svg/931629714a69e0cfcd4964486d307cb138a03126)
![{\displaystyle u(x,t)=_{C}1+\arctan(1/{\sqrt {(}}csc(_{C}3+C[1]*x+_{C}4*t)^{2}-1))*_{C}2}](http://wikimedia.org/api/rest_v1/media/math/render/svg/57efce97775e61f4d8e4160f875efb9d2babfe6d)
![{\displaystyle u(x,t)=_{C}1+\ln(\cos(_{C}3+C[1]*x+_{C}4*t)+{\sqrt {(}}\cos(_{C}3+C[1]*x+_{C}4*t)^{2}-1))*_{C}}](http://wikimedia.org/api/rest_v1/media/math/render/svg/3df00b982079cb0ec3538f1d041ab7c29046f7da)
![{\displaystyle u(x,t)=_{C}1+\ln(\cosh(_{C}3+C[1]*x+_{C}4*t)+{\sqrt {(}}\cosh(_{C}3+C[1]*x+_{C}4*t)^{2}-1))*_{C}2}](http://wikimedia.org/api/rest_v1/media/math/render/svg/e861422e79da247081d5a288f0ddac2b8e03e9bb)
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行波圖
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參考文獻
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