恰普雷金方程(英語:Chaplygin equation)是俄罗斯物理学家谢尔盖·阿列克谢耶维奇·恰普雷金在1904年发表的描写喷气流的非线性偏微分方程:[1]
![{\displaystyle u(x,t)=_{C}1+_{C}2*(_{C}3+C[1]*x+_{C}4*t)}](//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}](//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}](//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}}](//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}](//wikimedia.org/api/rest_v1/media/math/render/svg/e861422e79da247081d5a288f0ddac2b8e03e9bb)
![{\displaystyle u(x,t)=-(0.479e-2*(11400.+581.*\tan(1.02*t)+60300.*\exp(.833*x)+3060.*exp(.833*x)*\tan(1.02*t)+79000.*\exp(1.67*x)+4010.*\exp(1.67*x)*\tan(1.02*t)))*\exp(-.833*x)/(-10.+197.*\tan(1.02*t))}](//wikimedia.org/api/rest_v1/media/math/render/svg/46dfc5d23ea76dc7b8ddc550e1a7b337ef175bf1)
Chaplygin equation traveling wave plot
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Chaplygin equation traveling wave plot
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Chaplygin equation traveling wave plot
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Chaplygin equation traveling wave plot
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Chaplygin equation traveling wave plot
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Chaplygin equation traveling wave plot
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Chaplygin equation traveling wave plot
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Chaplygin equation traveling wave plot
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Chaplygin equation traveling wave plot
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Chaplygin equation traveling wave plot
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Andrei D. Polyanin,Valentin F. Zaitsev, HANDBOOK OF NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS, SECOND EDITION p765 CRC PRESS
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