正则长波方程(Regularized long wave equation)是一个非线性偏微分方程：
u_{t}+u_{x}+\alphauu_{x}-\mu*u_{txx}=0;
当 α=1，μ=1，正则长波方程即本杰明-博纳-马奥尼方程。
解析解
: {u(x, t) = -(_C5+_C4)/(\alpha_C4)+12\mu_C5_C4WeierstrassP(_C3+_C4x+_C5*t, _C2, _C1)/\alpha}
: {u(x, t) = (4\mu_C3_C2^2-_C3-_C2)/(\alpha_C2)+12\mu_C3_C2csch(_C1+_C2x+_C3t)^2/\alpha}
: {u(x, t) = (4\mu_C3_C2^2-_C3-_C2)/(\alpha_C2)-12\mu_C3_C2sech(_C1+_C2x+_C3t)^2/\alpha}
: {u(x, t) = -(4\mu_C3_C2^2+_C3+_C2)/(\alpha_C2)+12\mu_C3_C2csc(_C1+_C2x+_C3t)^2/\alpha}
: {u(x, t) = (-4\mu_C4_C3^2-_C4-_C3+8\mu_C4_C3^2_C1^2)/(\alpha_C3)-12\mu_C4_C3_C1^2JacobiCN(_C2+_C3x+_C4*t, _C1)^2/\alpha}
: {u(x, t) = (-4\mu_C4_C3^2-_C4-_C3+8\mu_C4_C3^2_C1^2)/(\alpha_C3)-12\mu_C4_C3(-1+_C1^2)JacobiNC(_C2+_C3x+_C4*t, _C1)^2/\alpha}
: {u(x, t) = -(4\mu_C4_C3^2_C1^2+_C4+_C3-8\mu_C4_C3^2)/(\alpha_C3)-12\mu_C4_C3JacobiDN(_C2+_C3x+_C4t, _C1)^2/\alpha}
: {u(x, t) = -(4\mu_C4_C3^2_C1^2+_C4+_C3-8\mu_C4_C3^2)/(\alpha_C3)+12\mu_C4_C3(-1+_C1^2)JacobiND(_C2+_C3x+_C4*t, _C1)^2/\alpha}
: {u(x, t) = -(4\mu_C4_C3^2_C1^2+4\mu_C4_C3^2+_C4+_C3)/(\alpha_C3)+12\mu_C4_C3JacobiNS(_C2+_C3x+_C4t, _C1)^2/\alpha}
: {u(x, t) = -(4\mu_C4_C3^2_C1^2+4\mu_C4_C3^2+_C4+_C3)/(\alpha_C3)+12\mu_C4_C3_C1^2JacobiSN(_C2+_C3x+_C4*t, _C1)^2/\alpha}
行波图
参考文献
#Graham W. Griffiths William E.Shiesser Traveling Wave Analysis of Partial Differential p135 Equations Academy Press
Richard H. Enns George C. McCGuire, Nonlinear Physics Birkhauser,1997
#Inna Shingareva, Carlos Lizárraga-Celaya,Solving Nonlinear Partial Differential Equations with Maple Springer.
#Eryk Infeld and George Rowlands,Nonlinear Waves,Solitons and Chaos,Cambridge 2000
#Saber Elaydi,An Introduction to Difference Equationns, Springer 2000
#Dongming Wang, Elimination Practice,Imperial College Press 2004
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