博欣内斯克方程是一个二元非线性偏微分方程：[1] ∂ 2 u ∂ t 2 − ∂ 2 u ∂ x 2 − ∂ 2 u 2 ∂ 2 y 2 + ∂ 4 u ∂ x 4 = 0 {\displaystyle {\frac {\partial ^{2}u}{\partial t^{2}}}-{\frac {\partial ^{2}u}{\partial x^{2}}}-{\frac {\partial ^{2}u^{2}}{\partial ^{2}y^{2}}}+{\frac {\partial ^{4}u}{\partial x^{4}}}=0} 博欣内斯克方程有如下行波解：[2] u ( x , t ) = ( 3 / 2 ∗ ( 1 − c 2 ) ) ∗ s e c h ( ( 1 / 2 ) ∗ ( 1 − c 2 ) ∗ ( x − c ∗ t ) ) 2 {\displaystyle u(x,t)=(3/2*(1-c^{2}))*sech((1/2)*{\sqrt {(1-c^{2})*(x-c*t))^{2}}}} u ( x , y , t ) = 4 ∗ k 4 + ω 2 − k 2 2 ∗ l 2 + 6 ∗ k 2 ∗ cosh ( k ( x + x 0 ) + l ∗ ( y + y 0 ) − ω ∗ t ) 2 l 2 {\displaystyle u(x,y,t)={\frac {4*k^{4}+\omega ^{2}-k^{2}}{2*l^{2}}}+6*k^{2}*{\frac {\cosh(k(x+x0)+l*(y+y0)-\omega *t)^{2}}{l^{2}}}} u ( x , y , t ) := ( 1 / 2 ) ∗ ( 4 ∗ k 4 ∗ c o s h ( k ∗ x + k ∗ x 0 + l ∗ y + l ∗ y 0 − ω ∗ t ) 2 + ω 2 ∗ c o s h ( k ∗ x + k ∗ x 0 + l ∗ y + l ∗ y 0 − ω ∗ t ) 2 − k 2 ∗ c o s h ( k ∗ x + k ∗ x 0 + l ∗ y + l ∗ y 0 − ω ∗ t ) 2 − 12 ∗ k 4 ) / ( c o s h ( k ∗ x + k ∗ x 0 + l ∗ y + l ∗ y 0 − ω ∗ t ) 2 ∗ l 2 ) {\displaystyle u(x,y,t):={\frac {(1/2)*(4*k^{4}*cosh(k*x+k*x0+l*y+l*y0-\omega *t)^{2}+\omega ^{2}*cosh(k*x+k*x0+l*y+l*y0-\omega *t)^{2}-k^{2}*cosh(k*x+k*x0+l*y+l*y0-\omega *t)^{2}-12*k^{4})}{/(cosh(k*x+k*x0+l*y+l*y0-\omega *t)^{2}*l^{2})}}} 参考文献Loading content...Loading related searches...Wikiwand - on Seamless Wikipedia browsing. On steroids.
