正則長波方程

正則長波方程(Regularized long wave equation)是一個非線性偏微分方程：

$u_{t}+u_{x}+\alpha *u*u_{x}-\mu *u_{txx}=0;$

當 α=1，μ=1，正則長波方程即班傑明-博納-馬奧尼方程。

解析解

${u(x,t)=-(_{C}5+_{C}4)/(\alpha *_{C}4)+12*\mu *_{C}5*_{C}4*WeierstrassP(_{C}3+_{C}4*x+_{C}5*t,_{C}2,_{C}1)/\alpha }$

${u(x,t)=(4*\mu *_{C}3*_{C}2^{2}-_{C}3-_{C}2)/(\alpha *_{C}2)+12*\mu *_{C}3*_{C}2*csch(_{C}1+_{C}2*x+_{C}3*t)^{2}/\alpha }$

${u(x,t)=(4*\mu *_{C}3*_{C}2^{2}-_{C}3-_{C}2)/(\alpha *_{C}2)-12*\mu *_{C}3*_{C}2*sech(_{C}1+_{C}2*x+_{C}3*t)^{2}/\alpha }$

${u(x,t)=-(4*\mu *_{C}3*_{C}2^{2}+_{C}3+_{C}2)/(\alpha *_{C}2)+12*\mu *_{C}3*_{C}2*csc(_{C}1+_{C}2*x+_{C}3*t)^{2}/\alpha }$

${u(x,t)=(-4*\mu *_{C}4*_{C}3^{2}-_{C}4-_{C}3+8*\mu *_{C}4*_{C}3^{2}*_{C}1^{2})/(\alpha *_{C}3)-12*\mu *_{C}4*_{C}3*_{C}1^{2}*JacobiCN(_{C}2+_{C}3*x+_{C}4*t,_{C}1)^{2}/\alpha }$

${u(x,t)=(-4*\mu *_{C}4*_{C}3^{2}-_{C}4-_{C}3+8*\mu *_{C}4*_{C}3^{2}*_{C}1^{2})/(\alpha *_{C}3)-12*\mu *_{C}4*_{C}3*(-1+_{C}1^{2})*JacobiNC(_{C}2+_{C}3*x+_{C}4*t,_{C}1)^{2}/\alpha }$

${u(x,t)=-(4*\mu *_{C}4*_{C}3^{2}*_{C}1^{2}+_{C}4+_{C}3-8*\mu *_{C}4*_{C}3^{2})/(\alpha *_{C}3)-12*\mu *_{C}4*_{C}3*JacobiDN(_{C}2+_{C}3*x+_{C}4*t,_{C}1)^{2}/\alpha }$

${u(x,t)=-(4*\mu *_{C}4*_{C}3^{2}*_{C}1^{2}+_{C}4+_{C}3-8*\mu *_{C}4*_{C}3^{2})/(\alpha *_{C}3)+12*\mu *_{C}4*_{C}3*(-1+_{C}1^{2})*JacobiND(_{C}2+_{C}3*x+_{C}4*t,_{C}1)^{2}/\alpha }$

${u(x,t)=-(4*\mu *_{C}4*_{C}3^{2}*_{C}1^{2}+4*\mu *_{C}4*_{C}3^{2}+_{C}4+_{C}3)/(\alpha *_{C}3)+12*\mu *_{C}4*_{C}3*JacobiNS(_{C}2+_{C}3*x+_{C}4*t,_{C}1)^{2}/\alpha }$

${u(x,t)=-(4*\mu *_{C}4*_{C}3^{2}*_{C}1^{2}+4*\mu *_{C}4*_{C}3^{2}+_{C}4+_{C}3)/(\alpha *_{C}3)+12*\mu *_{C}4*_{C}3*_{C}1^{2}*JacobiSN(_{C}2+_{C}3*x+_{C}4*t,_{C}1)^{2}/\alpha }$

行波圖

正則長波方程行波圖

正則長波方程行波圖

正則長波方程行波圖

正則長波方程行波圖

正則長波方程行波圖

正則長波方程行波圖

正則長波方程行波圖

正則長波方程行波圖

正則長波方程行波圖

正則長波方程行波圖

正則長波方程行波圖

正則長波方程行波圖

正則長波方程行波圖

正則長波方程行波圖

正則長波方程行波圖

正則長波方程行波圖

正則長波方程行波圖

正則長波方程行波圖

參考文獻

1. Graham W. Griffiths William E.Shiesser Traveling Wave Analysis of Partial Differential p135 Equations Academy Press
2. Richard H. Enns George C. McCGuire, Nonlinear Physics Birkhauser,1997
3. Inna Shingareva, Carlos Lizárraga-Celaya,Solving Nonlinear Partial Differential Equations with Maple Springer.
4. Eryk Infeld and George Rowlands,Nonlinear Waves,Solitons and Chaos,Cambridge 2000
5. Saber Elaydi,An Introduction to Difference Equationns, Springer 2000
6. Dongming Wang, Elimination Practice,Imperial College Press 2004
7. David Betounes, Partial Differential Equations for Computational Science: With Maple and Vector Analysis Springer, 1998 ISBN 9780387983004
8. George Articolo Partial Differential Equations & Boundary Value Problems with Maple V Academic Press 1998 ISBN 9780120644759