Karachawa方程是一个模拟有表面张力的水波运动的非线性偏微分方程:[1]
解析解[编辑]
![{\displaystyle u(x,t)=(1/676)*(-338*{\sqrt {(}}-13*\mu )*_{C}3-69*\mu ^{3})/\mu +(105/338)*\mu ^{2}*tanh(_{C}1-(1/26)*{\sqrt {(}}-13*\mu )*x+_{C}3*t)^{2}-(105/676)*\mu ^{2}*tanh(_{C}1-(1/26)*{\sqrt {(}}-13*\mu )*x+_{C}3*t)^{4}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d9270fb70cc4dba74a0bc6f0c67a74489291c9ce)
![{\displaystyle u(x,t)=(1/676)*(338*{\sqrt {(}}-13*\mu )*_{C}3-69*\mu ^{3})/\mu +(105/338)*\mu ^{2}*coth(_{C}1+(1/26)*{\sqrt {(}}-13*\mu )*x+_{C}3*t)^{2}-(105/676)*\mu ^{2}*coth(_{C}1+(1/26)*{\sqrt {(}}-13*\mu )*x+_{C}3*t)^{4}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fa4f462f0232fbfb67a5e8dc568f4a28a797c04d)
![{\displaystyle u(x,t)=(1/676)*(338*{\sqrt {(}}-13*\mu )*_{C}3-69*\mu ^{3})/\mu +(105/338)*\mu ^{2}*tanh(_{C}1+(1/26)*{\sqrt {(}}-13*\mu )*x+_{C}3*t)^{2}-(105/676)*\mu ^{2}*tanh(_{C}1+(1/26)*{\sqrt {(}}-13*\mu )*x+_{C}3*t)^{4}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/982d3fb142d19f3649224ec6f8e7a35254b2f70b)
![{\displaystyle u(x,t)=-(1/676)*(-338*{\sqrt {(}}13)*{\sqrt {(}}\mu )*_{C}3+69*\mu ^{3})/\mu -(105/338)*\mu ^{2}*cot(_{C}1-(1/26)*{\sqrt {(}}13)*{\sqrt {(}}\mu )*x+_{C}3*t)^{2}-(105/676)*\mu ^{2}*cot(_{C}1-(1/26)*{\sqrt {(}}13)*{\sqrt {(}}\mu )*x+_{C}3*t)^{4}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d7a40e0784faf2fe6e4fc504bc3d010b13d32c09)
![{\displaystyle u(x,t)=-(1/676)*(-338*{\sqrt {(}}13)*{\sqrt {(}}\mu )*_{C}3+69*\mu ^{3})/\mu -(105/338)*\mu ^{2}*tan(_{C}1-(1/26)*{\sqrt {(}}13)*{\sqrt {(}}\mu )*x+_{C}3*t)^{2}-(105/676)*\mu ^{2}*tan(_{C}1-(1/26)*{\sqrt {(}}13)*{\sqrt {(}}\mu )*x+_{C}3*t)^{4}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a552aff502ebb48d4a3bd6251af0ac3c23e5e3af)
![{\displaystyle u(x,t)=-(1/676)*(338*{\sqrt {(}}13)*{\sqrt {(}}\mu )*_{C}3+69*\mu ^{3})/\mu -(105/338)*\mu ^{2}*tan(_{C}1+(1/26)*{\sqrt {(}}13)*{\sqrt {(}}\mu )*x+_{C}3*t)^{2}-(105/676)*\mu ^{2}*tan(_{C}1+(1/26)*{\sqrt {(}}13)*{\sqrt {(}}\mu )*x+_{C}3*t)^{4}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/80ca1136b07afcd5880e0d85112caaac4c767b57)
![{\displaystyle u(x,t)=(1/209560)*(-(13/5)*(2015*\mu -(195*I)*\mu *{\sqrt {(}}31))^{(}3/2)*_{C}3-(4991/1300*(2015*\mu -(195*I)*\mu *{\sqrt {(}}31)))*\mu ^{3}+10478*{\sqrt {(}}2015*\mu -(195*I)*\mu *{\sqrt {(}}31))*_{C}3*\mu +961*\mu ^{4})/\mu ^{2}+(7/676)*\mu *((651/20)*\mu -(123/20*I)*\mu *{\sqrt {(}}31))*sech(_{C}1-(1/260)*{\sqrt {(}}2015*\mu -(195*I)*\mu *{\sqrt {(}}31))*x+_{C}3*t)^{2}-(651/1352)*\mu *((11/20)*\mu -(3/20*I)*\mu *{\sqrt {(}}31))*sech(_{C}1-(1/260)*{\sqrt {(}}2015*\mu -(195*I)*\mu *{\sqrt {(}}31))*x+_{C}3*t)^{4}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3cc3976be62e2f3b0646d3e6ec0b507bf896f92a)
![{\displaystyle u(x,t)=-(1/523900)*(-(13/2)*(2015*\mu +(195*I)*\mu *{\sqrt {(}}31))^{(}3/2)*_{C}3+(23529/650*(2015*\mu +(195*I)*\mu *{\sqrt {(}}31)))*\mu ^{3}-26195*{\sqrt {(}}2015*\mu +(195*I)*\mu *{\sqrt {(}}31))*_{C}3*\mu -175863*\mu ^{4})/(\mu *((21/10)*\mu +(3/10*I)*\mu *{\sqrt {(}}31)))+(-(217/338)*\mu ^{2}+(7/16900)*\mu *(2015*\mu +(195*I)*\mu *{\sqrt {(}}31)))*coth(_{C}1-(1/260)*{\sqrt {(}}2015*\mu +(195*I)*\mu *{\sqrt {(}}31))*x+_{C}3*t)^{2}-(651/1352)*\mu *((11/20)*\mu +(3/20*I)*\mu *{\sqrt {(}}31))*coth(_{C}1-(1/260)*{\sqrt {(}}2015*\mu +(195*I)*\mu *{\sqrt {(}}31))*x+_{C}3*t)^{4}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cacabd8a691a578f081e38741046261a109ca682)
![{\displaystyle p[46]:=8.0741721983973002048*10^{5}+11257.587038449976187*I+(1813.0402209066405653-19.865040422291120617*I)*JacobiNS(1.5250+1.7351587051052163701*x^{1}.25+1.9035752853902350521*t^{1}.25,0.21767841032926169436e-1-0.16688086862630055943e-1*I)^{1}.5-1199.5620*JacobiNS(1.5250+1.7351587051052163701*x^{1}.25+1.9035752853902350521*t^{1}.25,0.21767841032926169436e-1-0.16688086862630055943e-1*I)^{4}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/20f0a85e9e68c476b165d80bb4001f7cd1b5febb)
![{\displaystyle p[47]:=8.0741721983973002048*10^{5}+11257.587038449976187*I+(15.667532401561428902-15.998034611025966429*I)*JacobiSN(1.5250+1.7351587051052163701*x^{1}.25+1.9035752853902350521*t^{1}.25,0.21767841032926169436e-1-0.16688086862630055943e-1*I)^{1}.5+(0.48758338627653809364e-2+0.84722715715396426655e-2*I)*JacobiSN(1.5250+1.7351587051052163701*x^{1}.25+1.9035752853902350521*t^{1}.25,0.21767841032926169436e-1-0.16688086862630055943e-1*I)^{4}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/aeb9740d336282ec96008418dd53b69a070471ee)
行波图[编辑]
Karachawa equation traveling wave plot
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Karachawa equation traveling wave plot
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Karachawa equation traveling wave plot
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Karachawa equation traveling wave plot
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Karachawa equation traveling wave plot
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Karachawa equation traveling wave plot
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Karachawa equation traveling wave plot
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Karachawa equation traveling wave plot
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Karachawa equation traveling wave plot
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Karachawa equation traveling wave plot
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Karachawa equation traveling wave plot
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Karachawa equation traveling wave plot
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Karachawa equation traveling wave plot
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Karachawa equation traveling wave plot
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Karachawa equation traveling wave plot
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Karachawa equation traveling wave plot
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参考文献[编辑]
- ^ 李志斌编著 《非线性数学物理方程的行波解》 127页 科学出版社 2008
- *谷超豪 《孤立子理论中的达布变换及其几何应用》 上海科学技术出版社
- *阎振亚著 《复杂非线性波的构造性理论及其应用》 科学出版社 2007年
- 李志斌编著 《非线性数学物理方程的行波解》 科学出版社
- 王东明著 《消去法及其应用》 科学出版社 2002
- *何青 王丽芬编著 《Maple 教程》 科学出版社 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