KdV-mKdV方程是一个非线性偏微分方程:[1]
解析解[编辑]
![{\displaystyle u(x,t)=-1/(2*\beta )-{\sqrt {(}}\beta *\gamma *(-1+_{C}1^{2}))*_{C}3*JacobiNC(-_{C}2-_{C}3*x+(1/2)*_{C}3*(-2*\beta *\gamma *_{C}3^{2}+4*\beta *_{C}3^{2}*\gamma *_{C}1^{2}-3)*t/\beta ,_{C}1)/\beta }](https://wikimedia.org/api/rest_v1/media/math/render/svg/acca317d32593bc8766f3c67c29728648d38342f)
![{\displaystyle u(x,t)=-1/(2*\beta )+{\sqrt {(}}\beta *\gamma *(-1+_{C}1^{2}))*_{C}3*JacobiNC(-_{C}2-_{C}3*x+(1/2)*_{C}3*(-2*\beta *\gamma *_{C}3^{2}+4*\beta *_{C}3^{2}*\gamma *_{C}1^{2}-3)*t/\beta ,_{C}1)/\beta }](https://wikimedia.org/api/rest_v1/media/math/render/svg/e1d33c7340e6026dcb86c7e004ad8a6408b71507)
![{\displaystyle u(x,t)=-1/(2*\beta )-{\sqrt {(}}-\beta *\gamma *(-1+_{C}1^{2}))*_{C}3*JacobiND(_{C}2+_{C}3*x+(1/2)*_{C}3*(2*\beta *_{C}3^{2}*\gamma *_{C}1^{2}-4*\beta *\gamma *_{C}3^{2}+3)*t/\beta ,_{C}1)/\beta }](https://wikimedia.org/api/rest_v1/media/math/render/svg/1b67bba74d6cb33af3ec99a515663ad3caf29509)
![{\displaystyle u(x,t)=-1/(2*\beta )+{\sqrt {(}}-\beta *\gamma *(-1+_{C}1^{2}))*_{C}3*JacobiND(_{C}2+_{C}3*x+(1/2)*_{C}3*(2*\beta *_{C}3^{2}*\gamma *_{C}1^{2}-4*\beta *\gamma *_{C}3^{2}+3)*t/\beta ,_{C}1)/\beta }](https://wikimedia.org/api/rest_v1/media/math/render/svg/8388d8789b5d4517b734003e7e84aee25d3e0230)
![{\displaystyle u(x,t)=-1/(2*\beta )-\gamma *_{C}2*sech(_{C}1+_{C}2*x-(1/2)*_{C}2*(2*\beta *\gamma *_{C}2^{2}-3)*t/\beta )/{\sqrt {(}}\beta *\gamma )}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8a2ac2f2231ff5ea76bacd403473c167915aa1bf)
![{\displaystyle u(x,t)=-1/(2*\beta )-\gamma *_{C}3*JacobiDN(_{C}2+_{C}3*x+(1/2)*_{C}3*(2*\beta *_{C}3^{2}*\gamma *_{C}1^{2}-4*\beta *\gamma *_{C}3^{2}+3)*t/\beta ,_{C}1)/{\sqrt {(}}\beta *\gamma )}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d6db3a83fbccd871e9633c21b700b0ffd67ce169)
![{\displaystyle u(x,t)=-1/(2*\beta )-\gamma *_{C}2*cot(_{C}1+_{C}2*x-(1/2)*_{C}2*(4*\beta *\gamma *_{C}2^{2}-3)*t/\beta )/{\sqrt {(}}-\beta *\gamma )}](https://wikimedia.org/api/rest_v1/media/math/render/svg/02da9edba228e53cfed6d711dbb3c45d72767bf5)
![{\displaystyle u(x,t)=-1/(2*\beta )-\gamma *_{C}2*coth(_{C}1+_{C}2*x+(1/2)*_{C}2*(4*\beta *\gamma *_{C}2^{2}+3)*t/\beta )/{\sqrt {(}}-\beta *\gamma )}](https://wikimedia.org/api/rest_v1/media/math/render/svg/084950ace721e9cdb1c4333024d062449d4f8c81)
![{\displaystyle u(x,t)=-1/(2*\beta )-\gamma *_{C}2*csch(_{C}1+_{C}2*x-(1/2)*_{C}2*(2*\beta *\gamma *_{C}2^{2}-3)*t/\beta )/{\sqrt {(}}-\beta *\gamma )}](https://wikimedia.org/api/rest_v1/media/math/render/svg/206a04f7c1ee04080243c3b0ff7a1a826f6560e1)
![{\displaystyle u(x,t)=-1/(2*\beta )-\gamma *_{C}2*tan(_{C}1+_{C}2*x-(1/2)*_{C}2*(4*\beta *\gamma *_{C}2^{2}-3)*t/\beta )/{\sqrt {(}}-\beta *\gamma )}](https://wikimedia.org/api/rest_v1/media/math/render/svg/961a8eb885a05d530b349fd2d4f904bd3082e0e7)
![{\displaystyle u(x,t)=-1/(2*\beta )-\gamma *_{C}2*tanh(_{C}1+_{C}2*x+(1/2)*_{C}2*(4*\beta *\gamma *_{C}2^{2}+3)*t/\beta )/{\sqrt {(}}-\beta *\gamma )}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e5fb5a890ed3b39caae34804015f0c7651951ef8)
![{\displaystyle u(x,t)=-1/(2*\beta )-\gamma *_{C}3*JacobiNS(_{C}2+_{C}3*x+(1/2)*_{C}3*(2*\beta *\gamma *_{C}3^{2}+2*\beta *_{C}3^{2}*\gamma *_{C}1^{2}+3)*t/\beta ,_{C}1)/{\sqrt {(}}-\beta *\gamma )}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cc969954180db1b5dea78698c1c03001954267ef)
行波图[编辑]
Kdv-mKdv equation traveling wave plot
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Kdv-mKdv equation traveling wave plot
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Kdv-mKdv equation traveling wave plot
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Kdv-mKdv equation traveling wave plot
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Kdv-mKdv equation traveling wave plot
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Kdv-mKdv equation traveling wave plot
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Kdv-mKdv equation traveling wave plot
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Kdv-mKdv equation traveling wave plot
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Kdv-mKdv equation traveling wave plot
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Kdv-mKdv equation traveling wave plot
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Kdv-mKdv equation traveling wave plot
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Kdv-mKdv 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》 181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