非规范博欣内斯克方程(Unnormalized Boussinesq equation)是一个非线性偏微分方程:[1]
解析解
![{\displaystyle u(x,t)=_{C}5^{2}/(_{C}4^{2}*\alpha )-12*\beta *_{C}4^{2}*WeierstrassP(_{C}3+_{C}4*x+_{C}5*t,_{C}2,_{C}1)/\alpha }](https://wikimedia.org/api/rest_v1/media/math/render/svg/4c0351f941e8e10b13bb19e77aba616531dac37d)
![{\displaystyle u(x,t)=-(-_{C}3^{2}+4*\beta *_{C}2^{4})/(\alpha *_{C}2^{2})-12*\beta *_{C}2^{2}*csch(_{C}1+_{C}2*x+_{C}3*t)^{2}/\alpha }](https://wikimedia.org/api/rest_v1/media/math/render/svg/6200134bae94e659c502d1591109050e75e4f6b7)
![{\displaystyle u(x,t)=-(-_{C}3^{2}+4*\beta *_{C}2^{4})/(\alpha *_{C}2^{2})+12*\beta *_{C}2^{2}*sech(_{C}1+_{C}2*x+_{C}3*t)^{2}/\alpha }](https://wikimedia.org/api/rest_v1/media/math/render/svg/89d0c32932b05f55c18b7c60f405636165ba3823)
![{\displaystyle u(x,t)=-(-_{C}3^{2}+8*\beta *_{C}2^{4})/(\alpha *_{C}2^{2})-12*\beta *_{C}2^{2}*cot(_{C}1+_{C}2*x+_{C}3*t)^{2}/\alpha }](https://wikimedia.org/api/rest_v1/media/math/render/svg/ce3fa65d145a25864ac2be7596f78773b95dc966)
![{\displaystyle u(x,t)=-(-_{C}3^{2}+8*\beta *_{C}2^{4})/(\alpha *_{C}2^{2})-12*\beta *_{C}2^{2}*tan(_{C}1+_{C}2*x+_{C}3*t)^{2}/\alpha }](https://wikimedia.org/api/rest_v1/media/math/render/svg/679b777f75db36070dbf1a70f43070e6559a9f21)
![{\displaystyle u(x,t)=(_{C}3^{2}+4*\beta *_{C}2^{4})/(\alpha *_{C}2^{2})-12*\beta *_{C}2^{2}*csc(_{C}1+_{C}2*x+_{C}3*t)^{2}/\alpha }](https://wikimedia.org/api/rest_v1/media/math/render/svg/35828719697023ab8fd1d37e6707e88f204ae568)
![{\displaystyle u(x,t)=(_{C}3^{2}+4*\beta *_{C}2^{4})/(\alpha *_{C}2^{2})-12*\beta *_{C}2^{2}*sec(_{C}1+_{C}2*x+_{C}3*t)^{2}/\alpha }](https://wikimedia.org/api/rest_v1/media/math/render/svg/1db0eab244033d577d76a6da3a408849d3b43d5a)
![{\displaystyle u(x,t)=(_{C}3^{2}+8*\beta *_{C}2^{4})/(\alpha *_{C}2^{2})-12*\beta *_{C}2^{2}*coth(_{C}1+_{C}2*x+_{C}3*t)^{2}/\alpha }](https://wikimedia.org/api/rest_v1/media/math/render/svg/8ccc05c5f4f267e081b127bc0c06861168c32106)
![{\displaystyle u(x,t)=(_{C}3^{2}+8*\beta *_{C}2^{4})/(\alpha *_{C}2^{2})-12*\beta *_{C}2^{2}*tanh(_{C}1+_{C}2*x+_{C}3*t)^{2}/\alpha }](https://wikimedia.org/api/rest_v1/media/math/render/svg/b44461119d45c4d4e15ef889f4a8f613c0220ed1)
![{\displaystyle u(x,t)=(-8*\beta *_{C}3^{4}+_{C}4^{2}+4*\beta *_{C}3^{4}*_{C}1^{2})/(\alpha *_{C}3^{2})+12*\beta *_{C}3^{2}*JacobiDN(_{C}2+_{C}3*x+_{C}4*t,_{C}1)^{2}/\alpha }](https://wikimedia.org/api/rest_v1/media/math/render/svg/7db97528758ef6ff71eb546eae887e609808d208)
![{\displaystyle u(x,t)=(-8*\beta *_{C}3^{4}+_{C}4^{2}+4*\beta *_{C}3^{4}*_{C}1^{2})/(\alpha *_{C}3^{2})-12*\beta *_{C}3^{2}*(-1+_{C}1^{2})*JacobiND(_{C}2+_{C}3*x+_{C}4*t,_{C}1)^{2}/\alpha }](https://wikimedia.org/api/rest_v1/media/math/render/svg/d417b87ef92c5ce1033c28b182c7ecf6e1d27df4)
![{\displaystyle u(x,t)=(4*\beta *_{C}3^{4}*_{C}1^{2}+4*\beta *_{C}3^{4}+_{C}4^{2})/(\alpha *_{C}3^{2})-12*\beta *_{C}3^{2}*JacobiNS(_{C}2+_{C}3*x+_{C}4*t,_{C}1)^{2}/\alpha }](https://wikimedia.org/api/rest_v1/media/math/render/svg/a048a770c0dbc802672bb22ba46cec84dbf83964)
![{\displaystyle u(x,t)=(4*\beta *_{C}3^{4}*_{C}1^{2}+4*\beta *_{C}3^{4}+_{C}4^{2})/(\alpha *_{C}3^{2})-12*\beta *_{C}3^{2}*_{C}1^{2}*JacobiSN(_{C}2+_{C}3*x+_{C}4*t,_{C}1)^{2}/\alpha }](https://wikimedia.org/api/rest_v1/media/math/render/svg/007f3368d81b4cb997c4fc9ecb55b7958fa0ffc1)
![{\displaystyle u(x,t)=-(8*\beta *_{C}3^{4}*_{C}1^{2}-_{C}4^{2}-4*\beta *_{C}3^{4})/(\alpha *_{C}3^{2})+12*\beta *_{C}3^{2}*_{C}1^{2}*JacobiCN(_{C}2+_{C}3*x+_{C}4*t,_{C}1)^{2}/\alpha }](https://wikimedia.org/api/rest_v1/media/math/render/svg/0d7304efa488e1cd70b8a70d390fdcc9b332cfc7)
![{\displaystyle u(x,t)=-(8*\beta *_{C}3^{4}*_{C}1^{2}-_{C}4^{2}-4*\beta *_{C}3^{4})/(\alpha *_{C}3^{2})+12*\beta *_{C}3^{2}*(-1+_{C}1^{2})*JacobiNC(_{C}2+_{C}3*x+_{C}4*t,_{C}1)^{2}/\alpha }](https://wikimedia.org/api/rest_v1/media/math/render/svg/af04f2faa751db3fe0471783c6343e50018e0d00)
行波图
参考文献
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