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]
![{\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)
 Chaplygin equation traveling wave plot
|
 Chaplygin equation traveling wave plot
|
 Chaplygin equation traveling wave plot
|
 Chaplygin equation traveling wave plot
|
 Chaplygin equation traveling wave plot
|
 Chaplygin equation traveling wave plot
|
 Chaplygin equation traveling wave plot
|
 Chaplygin equation traveling wave plot
|
 Chaplygin equation traveling wave plot
|
 Chaplygin equation traveling wave plot
|
Andrei D. Polyanin,Valentin F. Zaitsev, HANDBOOK OF NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS, SECOND EDITION p765 CRC PRESS
- 谷超豪 《孤立子理論中的達布變換及其幾何應用》 上海科學技術出版社
- 閻振亞著 《複雜非線性波的構造性理論及其應用》 科學出版社 2007年
- 李志斌編著 《非線性數學物理方程的行波解》 科學出版社
- 王東明著 《消去法及其應用》 科學出版社 2002
- 何青 王麗芬編著 《Maple 教程》 科學出版社 2010 ISBN 9787030177445
- Graham W. Griffiths William E.Shiesser Traveling Wave Analysis of Partial Differential p135 Equations Academy Press
- Richard H. Enns George C. McCGuire, Nonlinear Physics Birkhauser,1997
- Inna Shingareva, Carlos Lizárraga-Celaya,Solving Nonlinear Partial Differential Equations with Maple Springer.
- Eryk Infeld and George Rowlands,Nonlinear Waves,Solitons and Chaos,Cambridge 2000
- Saber Elaydi,An Introduction to Difference Equationns, Springer 2000
- Dongming Wang, Elimination Practice,Imperial College Press 2004
- David Betounes, Partial Differential Equations for Computational Science: With Maple and Vector Analysis Springer, 1998 ISBN 9780387983004
- George Articolo Partial Differential Equations & Boundary Value Problems with Maple V Academic Press 1998 ISBN 9780120644759
![{\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)
