博欣内斯克型方程（Boussinesq type equation）是一个非线性偏微分方程：

u_{tt}-u_{xx}-2\alpha(uu_{x})_{x}-\betau_{xxtt}=0

解析解
: {u(x, t) = -(1/2)(-_C5^2+_C4^2)/(\alpha_C4^2)+6\beta_C5^2WeierstrassP(_C3+_C4x+_C5*t, _C2, _C1)/\alpha}
: {u(x, t) = -(1/2)(-_C3^2+8\beta_C3^2_C2^2+_C2^2)/(\alpha_C2^2)+6\beta_C3^2coth(_C1+_C2x+_C3t)^2/\alpha}
: u(x, t) = -(1/2)(-_C3^2+8\beta_C3^2_C2^2+_C2^2)/(\alpha_C2^2)+6\beta_C3^2tanh(_C1+_C2x+_C3t)^2/\alpha
: u(x, t) = (1/2)(_C3^2-_C2^2+4\beta_C3^2_C2^2)/(\alpha_C2^2)+6\beta_C3^2csch(_C1+_C2x+_C3t)^2/\alpha
: {u(x, t) = (1/2)(_C3^2-_C2^2+4\beta_C3^2_C2^2)/(\alpha_C2^2)-6\beta_C3^2sech(_C1+_C2x+_C3t)^2/\alpha}
: {u(x, t) = (1/2)(_C3^2+8\beta_C3^2_C2^2-_C2^2)/(\alpha_C2^2)+6\beta_C3^2cot(_C1+_C2x+_C3t)^2/\alpha}
: u(x, t) = (1/2)(-_C3^2+8\beta_C4^2_C3^2_C1^2-4\beta_C4^2_C3^2+_C4^2)/(\alpha_C3^2)-6\beta_C4^2_C1^2JacobiCN(_C2+_C3x+_C4*t, _C1)^2/\alpha
: u(x, t) = (1/2)(-_C3^2+8\beta_C4^2_C3^2_C1^2-4\beta_C4^2_C3^2+_C4^2)/(\alpha_C3^2)-6\beta_C4^2(-1+_C1^2)JacobiNC(_C2+_C3x+_C4*t, _C1)^2/\alpha
: {u(x, t) = -(1/2)(_C3^2-8\beta_C4^2_C3^2-_C4^2+4\beta_C4^2_C3^2_C1^2)/(\alpha_C3^2)-6\beta_C4^2JacobiDN(_C2+_C3x+_C4t, _C1)^2/\alpha}

行波图
参考文献

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