本傑明-博納-馬奧尼方程

本傑明 - 博納 - 馬奧尼方程(Benjamin–Bona–Mahony equation)是本傑明、博納和馬奧尼在1972年模擬流體力學中小振幅長波的非線性偏微分方程：

$u_{t}+u_{x}+uu_{x}-u_{xxt}=0.\,$

行波解

Benjamin–Bona–Mahony equation animation

BBM 方程有行波解.

$u(x,t)=-{\frac {8*_{C}2^{2}*_{C}3+_{C}3+_{C}2}{_{C}2}}+12*_{C}2*_{C}3*tanh(_{C}1+_{C}2*x+_{C}3*t)^{2}$

參數： _C3 = 5, _C2 =5，, _C1 = 5；

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參考文獻

• Avrin, Joel; Goldstein, Jerome A., Global existence for the Benjamin–Bona–Mahony equation in arbitrary dimensions., Nonlinear Anal., 1985, 9 (8): 861–865, MR 0799889, doi:10.1016/0362-546X(85)90023-9 
• Benjamin, T. B.; Bona, J. L.; Mahony, J. J., Model Equations for Long Waves in Nonlinear Dispersive Systems, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1972, 272 (1220): 47–78, Bibcode:1972RSPTA.272...47B, ISSN 0962-8428, JSTOR 74079, doi:10.1098/rsta.1972.0032 
• Zwillinger, Daniel, Handbook of differential equations 3rd, Boston, MA: Academic Press, Inc.: 174, 176, 1998, ISBN 978-0-12-784396-4, MR 0977062