MKdV方程

mKdV方程是一個非線性偏微分方程：^[1]

${\displaystyle u_{t}+6*u^{2}*u_{x}+u_{xxx}=0}$

解析解

${\displaystyle u(x,t)={\sqrt {(}}6)*_{C}2*sech(_{C}1+_{C}2*x-_{C}2^{3}*t)}$

${\displaystyle u(x,t)={\sqrt {(}}6)*_{C}3*JacobiDN(_{C}2+_{C}3*x+(-2*_{C}3^{3}+_{C}3^{3}*_{C}1^{2})*t,_{C}1)}$

${\displaystyle u(x,t)={\sqrt {(}}-6+6*_{C}1^{2})*_{C}3*JacobiNC(-_{C}2-_{C}3*x-(_{C}3^{3}-2*_{C}3^{3}*_{C}1^{2})*t,_{C}1)}$

${\displaystyle u(x,t)={\sqrt {(}}6-6*_{C}1^{2})*_{C}3*JacobiND(_{C}2+_{C}3*x+(-2*_{C}3^{3}+_{C}3^{3}*_{C}1^{2})*t,_{C}1)}$

${\displaystyle u(x,t)={\sqrt {(}}6)*_{C}1*_{C}3*JacobiCN(-_{C}2-_{C}3*x-(_{C}3^{3}-2*_{C}3^{3}*_{C}1^{2})*t,_{C}1)}$

${\displaystyle u(x,t)=-I*{\sqrt {(}}6)*_{C}2*cot(_{C}1+_{C}2*x-2*_{C}2^{3}*t)}$

${\displaystyle u(x,t)=-I*{\sqrt {(}}6)*_{C}2*coth(_{C}1+_{C}2*x+2*_{C}2^{3}*t)}$

${\displaystyle u(x,t)=-I*{\sqrt {(}}6)*_{C}2*csc(_{C}1+_{C}2*x+_{C}2^{3}*t)}$

${\displaystyle u(x,t)=-I*{\sqrt {(}}6)*_{C}2*tanh(_{C}1+_{C}2*x+2*_{C}2^{3}*t)}$

${\displaystyle u(x,t)=-I*{\sqrt {(}}6)*_{C}2*sec(_{C}1+_{C}2*x+_{C}2^{3}*t)}$

${\displaystyle u(x,t)=-I*{\sqrt {(}}6)*_{C}2*csch(_{C}1+_{C}2*x-_{C}2^{3}*t)}$

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行波圖

mKdV equation traveling wave plot

mKdV equation traveling wave plot

mKdV equation traveling wave plot

mKdV equation traveling wave plot

mKdV equation traveling wave plot

mKdV equation traveling wave plot

mKdV equation traveling wave plot

mKdV equation traveling wave plot

mKdV equation traveling wave plot

mKdV equation traveling wave plot

mKdV equation traveling wave plot

mKdV equation traveling wave plot

mKdV equation traveling wave plot

mKdV equation traveling wave plot

mKdV equation traveling wave plot

mKdV equation traveling wave plot

mKdV equation traveling wave plot

mKdV equation traveling wave plot

mKdV equation traveling wave plot

mKdV equation traveling wave plot