KdV-Burgers 也稱Burgers-KdV方程 是一個非線性偏微分方程：[ 1] [ 2]
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{\displaystyle u_{t}+u*u_{x}-\alpha *u_{xx}-\beta *u_{xxx}=0}
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{\displaystyle u(x,t)=(1/25)*(-3+250*\beta ^{2}*_{C}3)/\beta +(6/25)*coth(_{C}1-(1/10)*x/\beta +_{C}3*t)/\beta +(3/25)*coth(_{C}1-(1/10)*x/\beta +_{C}3*t)^{2}/\beta }
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{\displaystyle u(x,t)=(1/25)*(-3+250*\beta ^{2}*_{C}3)/\beta +(6/25)*tanh(_{C}1-(1/10)*x/\beta +_{C}3*t)/\beta +(3/25)*tanh(_{C}1-(1/10)*x/\beta +_{C}3*t)^{2}/\beta }
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{\displaystyle u(x,t)=-(1/25)*(3+250*\beta ^{2}*_{C}3)/\beta -(6/25)*tanh(_{C}1+(1/10)*x/\beta +_{C}3*t)/\beta +(3/25)*tanh(_{C}1+(1/10)*x/\beta +_{C}3*t)^{2}/\beta }
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{\displaystyle u(x,t)=(1/25)*(-(250*I)*\beta ^{2}*_{C}3-3)/\beta -(6/25*I)*tan(_{C}1-(1/10*I)*x/\beta +_{C}3*t)/\beta -(3/25)*tan(_{C}1-(1/10*I)*x/\beta +_{C}3*t)^{2}/\beta }
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{\displaystyle u(x,t)=(1/25)*(-(250*I)*\beta ^{2}*_{C}3-3)/\beta +(6/25*I)*cot(_{C}1-(1/10*I)*x/\beta +_{C}3*t)/\beta -(3/25)*cot(_{C}1-(1/10*I)*x/\beta +_{C}3*t)^{2}/\beta }
KdV-Burgers equation traveling wave plot KdV-Burgers equation traveling wave plot KdV-Burgers equation traveling wave plot KdV-Burgers equation traveling wave plot
KdV-Burgers equation traveling wave plot 2 KdV-Burgers equation traveling wave plot KdV-Burgers equation traveling wave plot KdV-Burgers equation traveling wave plot
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^ Shu, Jian-Jun. The proper analytical solution of the Korteweg-de Vries-Burgers equation. Journal of Physics A-Mathematical and General. 1987, 20 (2): 49–56. doi:10.1088/0305-4470/20/2/002 ^ 李志斌編著 《非線性數學物理方程的行波解》 61頁 科學出版社 2008
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