亨特 - 萨克斯顿方程

亨特 - 萨克斯顿方程(Hunter–Saxton equation)是一个模拟向列型液晶中波动传播的非线性偏微分方程： ( u t + u u x ) x = 1 2 u x 2 {\displaystyle (u_{t}+uu_{x})_{x}={\frac {1}{2}}\,u_{x}^{2}} 亨特 - 萨克斯顿方程有解析解： u ( x , t ) = 1 1 − t / 2 ∗ ( x − t ) + 1 {\displaystyle u(x,t)={\frac {1}{1-t/2}}*(x-t)+1} 此外，Maple软件包 TWSolution 给出多个行波解： tanh 展开法 f 1 := u ( x , t ) = − 1.7045454545454545454 + 1.1363636363636363636 ∗ ( − ( 1 / 4 ) ∗ ( 6.336 ∗ l n ( t a n h ( 2.3 + .88 ∗ x + 1.5 ∗ t ) − 1 ) − 6.336 ∗ l n ( t a n h ( 2.3 + .88 ∗ x + 1.5 ∗ t ) + 1 ) + 9.2928 ) ( 1 / 3 ) − ( 1 / 4 ∗ I ) ∗ s q r t ( 3 ) ∗ ( 6.336 ∗ l n ( t a n h ( 2.3 + .88 ∗ x + 1.5 ∗ t ) − 1 ) − 6.336 ∗ l n ( t a n h ( 2.3 + .88 ∗ x + 1.5 ∗ t ) + 1 ) + 9.2928 ) ( 1 / 3 ) ) 2 {\displaystyle f1:=u(x,t)=-1.7045454545454545454+1.1363636363636363636*(-(1/4)*(6.336*ln(tanh(2.3+.88*x+1.5*t)-1)-6.336*ln(tanh(2.3+.88*x+1.5*t)+1)+9.2928)^{(}1/3)-(1/4*I)*sqrt(3)*(6.336*ln(tanh(2.3+.88*x+1.5*t)-1)-6.336*ln(tanh(2.3+.88*x+1.5*t)+1)+9.2928)^{(}1/3))^{2}} f 2 := u ( x , t ) = − 1.7045454545454545454 + 1.1363636363636363636 ∗ ( − ( 1 / 4 ) ∗ ( 6.336 ∗ l n ( t a n h ( 2.3 + .88 ∗ x + 1.5 ∗ t ) − 1 ) − 6.336 ∗ l n ( t a n h ( 2.3 + .88 ∗ x + 1.5 ∗ t ) + 1 ) + 9.2928 ) ( 1 / 3 ) + ( 1 / 4 ∗ I ) ∗ s q r t ( 3 ) ∗ ( 6.336 ∗ l n ( t a n h ( 2.3 + .88 ∗ x + 1.5 ∗ t ) − 1 ) − 6.336 ∗ l n ( t a n h ( 2.3 + .88 ∗ x + 1.5 ∗ t ) + 1 ) + 9.2928 ) ( 1 / 3 ) ) 2 {\displaystyle f2:=u(x,t)=-1.7045454545454545454+1.1363636363636363636*(-(1/4)*(6.336*ln(tanh(2.3+.88*x+1.5*t)-1)-6.336*ln(tanh(2.3+.88*x+1.5*t)+1)+9.2928)^{(}1/3)+(1/4*I)*sqrt(3)*(6.336*ln(tanh(2.3+.88*x+1.5*t)-1)-6.336*ln(tanh(2.3+.88*x+1.5*t)+1)+9.2928)^{(}1/3))^{2}} u ( x , t ) = − 1.7045454545454545454 + 0.28409090909090909090 ( 6.336 l n ( t a n h ( 2.3 + 0.88 x + 1.5 t ) − 1 ) − 6.336 l n ( t a n h ( 2.3 + 0.88 x + 1.5 t ) + 1 ) + 9.2928 ) ( 2 / 3 ) {\displaystyle u(x,t)=-1.7045454545454545454+0.28409090909090909090(6.336ln(tanh(2.3+0.88x+1.5t)-1)-6.336ln(tanh(2.3+0.88x+1.5t)+1)+9.2928)^{(}2/3)} 其中 f1、f2 是重解，因此，只有两个独立的行波解。 sech arctan 展开法 f [ 1 ] := − .20000000000000000000 + ( 1 / 12 ) ∗ ( − ( 36 ∗ ( 1.3 ∗ a r c t a n ( 1 / s q r t ( s e c h ( 2 + 3 ∗ x + .6 ∗ t ) 2 − 1 ) ) ∗ s q r t ( s e c h ( 2 + 3 ∗ x + .6 ∗ t ) + 1 ) ∗ s q r t ( s e c h ( 2 + 3 ∗ x + .6 ∗ t ) − 1 ) − 2.6 ∗ s q r t ( s e c h ( 2 + 3 ∗ x + .6 ∗ t ) 2 − 1 ) ) ) / s q r t ( s e c h ( 2 + 3 ∗ x + .6 ∗ t ) 2 − 1 ) ) ( 2 / 3 ) {\displaystyle f[1]:=-.20000000000000000000+(1/12)*(-(36*(1.3*arctan(1/sqrt(sech(2+3*x+.6*t)^{2}-1))*sqrt(sech(2+3*x+.6*t)+1)*sqrt(sech(2+3*x+.6*t)-1)-2.6*sqrt(sech(2+3*x+.6*t)^{2}-1)))/sqrt(sech(2+3*x+.6*t)^{2}-1))^{(}2/3)} f [ 2 ] := − .20000000000000000000 + ( 1 / 3 ) ∗ ( − ( 1 / 4 ) ∗ ( − ( 36 ∗ ( 1.3 ∗ a r c t a n ( 1 / s q r t ( s e c h ( 2 + 3 ∗ x + .6 ∗ t ) 2 − 1 ) ) ∗ s q r t ( s e c h ( 2 + 3 ∗ x + .6 ∗ t ) + 1 ) ∗ s q r t ( s e c h ( 2 + 3 ∗ x + .6 ∗ t ) − 1 ) − 2.6 ∗ s q r t ( s e c h ( 2 + 3 ∗ x + .6 ∗ t ) 2 − 1 ) ) ) / s q r t ( s e c h ( 2 + 3 ∗ x + .6 ∗ t ) 2 − 1 ) ) ( 1 / 3 ) − ( 1 / 4 ∗ I ) ∗ s q r t ( 3 ) ∗ ( − ( 36 ∗ ( 1.3 ∗ a r c t a n ( 1 / s q r t ( s e c h ( 2 + 3 ∗ x + .6 ∗ t ) 2 − 1 ) ) ∗ s q r t ( s e c h ( 2 + 3 ∗ x + .6 ∗ t ) + 1 ) ∗ s q r t ( s e c h ( 2 + 3 ∗ x + .6 ∗ t ) − 1 ) − 2.6 ∗ s q r t ( s e c h ( 2 + 3 ∗ x + .6 ∗ t ) 2 − 1 ) ) ) / s q r t ( s e c h ( 2 + 3 ∗ x + .6 ∗ t ) 2 − 1 ) ) ( 1 / 3 ) ) 2 {\displaystyle f[2]:=-.20000000000000000000+(1/3)*(-(1/4)*(-(36*(1.3*arctan(1/sqrt(sech(2+3*x+.6*t)^{2}-1))*sqrt(sech(2+3*x+.6*t)+1)*sqrt(sech(2+3*x+.6*t)-1)-2.6*sqrt(sech(2+3*x+.6*t)^{2}-1)))/sqrt(sech(2+3*x+.6*t)^{2}-1))^{(}1/3)-(1/4*I)*sqrt(3)*(-(36*(1.3*arctan(1/sqrt(sech(2+3*x+.6*t)^{2}-1))*sqrt(sech(2+3*x+.6*t)+1)*sqrt(sech(2+3*x+.6*t)-1)-2.6*sqrt(sech(2+3*x+.6*t)^{2}-1)))/sqrt(sech(2+3*x+.6*t)^{2}-1))^{(}1/3))^{2}} f [ 3 ] := − .20000000000000000000 + ( 1 / 3 ) ∗ ( − ( 1 / 4 ) ∗ ( − ( 36 ∗ ( 1.3 ∗ a r c t a n ( 1 / s q r t ( s e c h ( 2 + 3 ∗ x + .6 ∗ t ) 2 − 1 ) ) ∗ s q r t ( s e c h ( 2 + 3 ∗ x + .6 ∗ t ) + 1 ) ∗ s q r t ( s e c h ( 2 + 3 ∗ x + .6 ∗ t ) − 1 ) − 2.6 ∗ s q r t ( s e c h ( 2 + 3 ∗ x + .6 ∗ t ) 2 − 1 ) ) ) / s q r t ( s e c h ( 2 + 3 ∗ x + .6 ∗ t ) 2 − 1 ) ) ( 1 / 3 ) + ( 1 / 4 ∗ I ) ∗ s q r t ( 3 ) ∗ ( − ( 36 ∗ ( 1.3 ∗ a r c t a n ( 1 / s q r t ( s e c h ( 2 + 3 ∗ x + .6 ∗ t ) 2 − 1 ) ) ∗ s q r t ( s e c h ( 2 + 3 ∗ x + .6 ∗ t ) + 1 ) ∗ s q r t ( s e c h ( 2 + 3 ∗ x + .6 ∗ t ) − 1 ) − 2.6 ∗ s q r t ( s e c h ( 2 + 3 ∗ x + .6 ∗ t ) 2 − 1 ) ) ) / s q r t ( s e c h ( 2 + 3 ∗ x + .6 ∗ t ) 2 − 1 ) ) ( 1 / 3 ) ) 2 {\displaystyle f[3]:=-.20000000000000000000+(1/3)*(-(1/4)*(-(36*(1.3*arctan(1/sqrt(sech(2+3*x+.6*t)^{2}-1))*sqrt(sech(2+3*x+.6*t)+1)*sqrt(sech(2+3*x+.6*t)-1)-2.6*sqrt(sech(2+3*x+.6*t)^{2}-1)))/sqrt(sech(2+3*x+.6*t)^{2}-1))^{(}1/3)+(1/4*I)*sqrt(3)*(-(36*(1.3*arctan(1/sqrt(sech(2+3*x+.6*t)^{2}-1))*sqrt(sech(2+3*x+.6*t)+1)*sqrt(sech(2+3*x+.6*t)-1)-2.6*sqrt(sech(2+3*x+.6*t)^{2}-1)))/sqrt(sech(2+3*x+.6*t)^{2}-1))^{(}1/3))^{2}} f [ 4 ] := − .20000000000000000000 + ( 1 / 3 ) ∗ ( − ( 1 / 4 ) ∗ ( 187.2 + 140.4 ∗ x + 28.08 ∗ t ) ( 1 / 3 ) − ( 1 / 4 ∗ I ) ∗ s q r t ( 3 ) ∗ ( 187.2 + 140.4 ∗ x + 28.08 ∗ t ) ( 1 / 3 ) ) 2 {\displaystyle f[4]:=-.20000000000000000000+(1/3)*(-(1/4)*(187.2+140.4*x+28.08*t)^{(}1/3)-(1/4*I)*sqrt(3)*(187.2+140.4*x+28.08*t)^{(}1/3))^{2}} f [ 5 ] := − .20000000000000000000 + ( 1 / 3 ) ∗ ( − ( 1 / 4 ) ∗ ( 187.2 + 140.4 ∗ x + 28.08 ∗ t ) ( 1 / 3 ) + ( 1 / 4 ∗ I ) ∗ s q r t ( 3 ) ∗ ( 187.2 + 140.4 ∗ x + 28.08 ∗ t ) ( 1 / 3 ) ) 2 {\displaystyle f[5]:=-.20000000000000000000+(1/3)*(-(1/4)*(187.2+140.4*x+28.08*t)^{(}1/3)+(1/4*I)*sqrt(3)*(187.2+140.4*x+28.08*t)^{(}1/3))^{2}} f [ 6 ] := − .20000000000000000000 + ( 1 / 12 ) ∗ ( 187.2 + 140.4 ∗ x + 28.08 ∗ t ) ( 2 / 3 ) {\displaystyle f[6]:=-.20000000000000000000+(1/12)*(187.2+140.4*x+28.08*t)^{(}2/3)} < f [ 7 ] := − 1.6666666666666666667 ∗ C 6 + 1.6666666666666666667 ∗ ( − ( 1 / 4 ) ∗ ( 9.36 ∗ I n t a t ( 1 / s q r t ( 4 ∗ a 4 − 5 ∗ a 2 + 1 ) , a = J a c o b i S N ( 3 + .6 ∗ x + C 6 ∗ t , 2 ) ) + 18.72 ) ( 1 / 3 ) − ( 1 / 4 ∗ I ) ∗ s q r t ( 3 ) ∗ ( 9.36 ∗ I n t a t ( 1 / s q r t ( 4 ∗ a 4 − 5 ∗ a 2 + 1 ) , a = J a c o b i S N ( 3 + .6 ∗ x + C 6 ∗ t , 2 ) ) + 18.72 ) ( 1 / 3 ) ) 2 {\displaystyle <f[7]:=-1.6666666666666666667*_{C}6+1.6666666666666666667*(-(1/4)*(9.36*Intat(1/sqrt(4*_{a}^{4}-5*_{a}^{2}+1),_{a}=JacobiSN(3+.6*x+_{C}6*t,2))+18.72)^{(}1/3)-(1/4*I)*sqrt(3)*(9.36*Intat(1/sqrt(4*_{a}^{4}-5*_{a}^{2}+1),_{a}=JacobiSN(3+.6*x+_{C}6*t,2))+18.72)^{(}1/3))^{2}} f [ 8 ] := − 1.6666666666666666667 ∗ C 6 + 1.6666666666666666667 ∗ ( − ( 1 / 4 ) ∗ ( 9.36 ∗ I n t a t ( 1 / s q r t ( 4 ∗ a 4 − 5 ∗ a 2 + 1 ) , a = J a c o b i S N ( 3 + .6 ∗ x + C 6 ∗ t , 2 ) ) + 18.72 ) ( 1 / 3 ) + ( 1 / 4 ∗ I ) ∗ s q r t ( 3 ) ∗ ( 9.36 ∗ I n t a t ( 1 / s q r t ( 4 ∗ a 4 − 5 ∗ a 2 + 1 ) , a = J a c o b i S N ( 3 + .6 ∗ x + C 6 ∗ t , 2 ) ) + 18.72 ) ( 1 / 3 ) ) 2 {\displaystyle f[8]:=-1.6666666666666666667*_{C}6+1.6666666666666666667*(-(1/4)*(9.36*Intat(1/sqrt(4*_{a}^{4}-5*_{a}^{2}+1),_{a}=JacobiSN(3+.6*x+_{C}6*t,2))+18.72)^{(}1/3)+(1/4*I)*sqrt(3)*(9.36*Intat(1/sqrt(4*_{a}^{4}-5*_{a}^{2}+1),_{a}=JacobiSN(3+.6*x+_{C}6*t,2))+18.72)^{(}1/3))^{2}} f [ 9 ] := − 1.6666666666666666667 ∗ C 6 + .41666666666666666668 ∗ ( 9.36 ∗ I n t a t ( 1 / s q r t ( 4 ∗ a 4 − 5 ∗ a 2 + 1 ) , a = J a c o b i S N ( 3 + .6 ∗ x + C 6 ∗ t , 2 ) ) + 18.72 ) ( 2 / 3 ) {\displaystyle f[9]:=-1.6666666666666666667*_{C}6+.41666666666666666668*(9.36*Intat(1/sqrt(4*_{a}^{4}-5*_{a}^{2}+1),_{a}=JacobiSN(3+.6*x+_{C}6*t,2))+18.72)^{(}2/3)} f1 f2 f3 f4 f5 f6 File:Hunter Saxton extended plot1.gif 综合展开 p [ 12 ] := − 1.0714 + .71429 ∗ ( − .50821 ∗ ( ( 1.1 ∗ l n ( c o s ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + s q r t ( c o s ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) 2 − 1. ) ) ∗ s q r t ( ( c o s ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) − 1. ) ∗ ( c o s ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + 1. ) ) + 1.2 ∗ s q r t ( c o s ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + 1. ) ∗ s q r t ( c o s ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) − 1. ) ) ∗ ( 1. + s q r t ( 1 / ( ( c o s ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) − 1. ) ∗ ( c o s ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + 1. ) ) ) ∗ s q r t ( c o s ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) − 1. ) ∗ s q r t ( c o s ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + 1. ) ) / ( s q r t ( c o s ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + 1. ) ∗ s q r t ( c o s ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) − 1. ) ) ) ( 1 / 3 ) − ( .88026 ∗ I ) ∗ ( ( 1.1 ∗ l n ( c o s ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + s q r t ( c o s ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) 2 − 1. ) ) ∗ s q r t ( ( c o s ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) − 1. ) ∗ ( c o s ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + 1. ) ) + 1.2 ∗ s q r t ( c o s ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + 1. ) ∗ s q r t ( c o s ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) − 1. ) ) ∗ ( 1. + s q r t ( 1 / ( ( c o s ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) − 1. ) ∗ ( c o s ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + 1. ) ) ) ∗ s q r t ( c o s ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) − 1. ) ∗ s q r t ( c o s ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + 1. ) ) / ( s q r t ( c o s ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + 1. ) ∗ s q r t ( c o s ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) − 1. ) ) ) ( 1 / 3 ) ) 2 {\displaystyle p[12]:=-1.0714+.71429*(-.50821*((1.1*ln(cos(1.3+1.4*x+1.5*t)+sqrt(cos(1.3+1.4*x+1.5*t)^{2}-1.))*sqrt((cos(1.3+1.4*x+1.5*t)-1.)*(cos(1.3+1.4*x+1.5*t)+1.))+1.2*sqrt(cos(1.3+1.4*x+1.5*t)+1.)*sqrt(cos(1.3+1.4*x+1.5*t)-1.))*(1.+sqrt(1/((cos(1.3+1.4*x+1.5*t)-1.)*(cos(1.3+1.4*x+1.5*t)+1.)))*sqrt(cos(1.3+1.4*x+1.5*t)-1.)*sqrt(cos(1.3+1.4*x+1.5*t)+1.))/(sqrt(cos(1.3+1.4*x+1.5*t)+1.)*sqrt(cos(1.3+1.4*x+1.5*t)-1.)))^{(}1/3)-(.88026*I)*((1.1*ln(cos(1.3+1.4*x+1.5*t)+sqrt(cos(1.3+1.4*x+1.5*t)^{2}-1.))*sqrt((cos(1.3+1.4*x+1.5*t)-1.)*(cos(1.3+1.4*x+1.5*t)+1.))+1.2*sqrt(cos(1.3+1.4*x+1.5*t)+1.)*sqrt(cos(1.3+1.4*x+1.5*t)-1.))*(1.+sqrt(1/((cos(1.3+1.4*x+1.5*t)-1.)*(cos(1.3+1.4*x+1.5*t)+1.)))*sqrt(cos(1.3+1.4*x+1.5*t)-1.)*sqrt(cos(1.3+1.4*x+1.5*t)+1.))/(sqrt(cos(1.3+1.4*x+1.5*t)+1.)*sqrt(cos(1.3+1.4*x+1.5*t)-1.)))^{(}1/3))^{2}} p [ 13 ] := − 1.0714 + .71429 ∗ ( − .50821 ∗ ( ( 1.1 ∗ l n ( c o s ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + s q r t ( c o s ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) 2 − 1. ) ) ∗ s q r t ( ( c o s ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) − 1. ) ∗ ( c o s ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + 1. ) ) + 1.2 ∗ s q r t ( c o s ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + 1. ) ∗ s q r t ( c o s ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) − 1. ) ) ∗ ( 1. + s q r t ( 1 / ( ( c o s ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) − 1. ) ∗ ( c o s ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + 1. ) ) ) ∗ s q r t ( c o s ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) − 1. ) ∗ s q r t ( c o s ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + 1. ) ) / ( s q r t ( c o s ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + 1. ) ∗ s q r t ( c o s ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) − 1. ) ) ) ( 1 / 3 ) + ( .88026 ∗ I ) ∗ ( ( 1.1 ∗ l n ( c o s ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + s q r t ( c o s ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) 2 − 1. ) ) ∗ s q r t ( ( c o s ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) − 1. ) ∗ ( c o s ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + 1. ) ) + 1.2 ∗ s q r t ( c o s ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + 1. ) ∗ s q r t ( c o s ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) − 1. ) ) ∗ ( 1. + s q r t ( 1 / ( ( c o s ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) − 1. ) ∗ ( c o s ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + 1. ) ) ) ∗ s q r t ( c o s ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) − 1. ) ∗ s q r t ( c o s ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + 1. ) ) / ( s q r t ( c o s ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + 1. ) ∗ s q r t ( c o s ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) − 1. ) ) ) ( 1 / 3 ) ) 2 {\displaystyle p[13]:=-1.0714+.71429*(-.50821*((1.1*ln(cos(1.3+1.4*x+1.5*t)+sqrt(cos(1.3+1.4*x+1.5*t)^{2}-1.))*sqrt((cos(1.3+1.4*x+1.5*t)-1.)*(cos(1.3+1.4*x+1.5*t)+1.))+1.2*sqrt(cos(1.3+1.4*x+1.5*t)+1.)*sqrt(cos(1.3+1.4*x+1.5*t)-1.))*(1.+sqrt(1/((cos(1.3+1.4*x+1.5*t)-1.)*(cos(1.3+1.4*x+1.5*t)+1.)))*sqrt(cos(1.3+1.4*x+1.5*t)-1.)*sqrt(cos(1.3+1.4*x+1.5*t)+1.))/(sqrt(cos(1.3+1.4*x+1.5*t)+1.)*sqrt(cos(1.3+1.4*x+1.5*t)-1.)))^{(}1/3)+(.88026*I)*((1.1*ln(cos(1.3+1.4*x+1.5*t)+sqrt(cos(1.3+1.4*x+1.5*t)^{2}-1.))*sqrt((cos(1.3+1.4*x+1.5*t)-1.)*(cos(1.3+1.4*x+1.5*t)+1.))+1.2*sqrt(cos(1.3+1.4*x+1.5*t)+1.)*sqrt(cos(1.3+1.4*x+1.5*t)-1.))*(1.+sqrt(1/((cos(1.3+1.4*x+1.5*t)-1.)*(cos(1.3+1.4*x+1.5*t)+1.)))*sqrt(cos(1.3+1.4*x+1.5*t)-1.)*sqrt(cos(1.3+1.4*x+1.5*t)+1.))/(sqrt(cos(1.3+1.4*x+1.5*t)+1.)*sqrt(cos(1.3+1.4*x+1.5*t)-1.)))^{(}1/3))^{2}} p [ 16 ] := − 1.0714 + .71429 ∗ ( − .50821 ∗ ( ( 1.1 ∗ l n ( s i n ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + s q r t ( s i n ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) 2 − 1. ) ) ∗ s q r t ( ( s i n ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) − 1. ) ∗ ( s i n ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + 1. ) ) + 1.2 ∗ s q r t ( s i n ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + 1. ) ∗ s q r t ( s i n ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) − 1. ) ) ∗ ( 1. + s q r t ( 1 / ( ( s i n ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) − 1. ) ∗ ( s i n ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + 1. ) ) ) ∗ s q r t ( s i n ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) − 1. ) ∗ s q r t ( s i n ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + 1. ) ) / ( s q r t ( s i n ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + 1. ) ∗ s q r t ( s i n ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) − 1. ) ) ) ( 1 / 3 ) − ( .88026 ∗ I ) ∗ ( ( 1.1 ∗ l n ( s i n ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + s q r t ( s i n ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) 2 − 1. ) ) ∗ s q r t ( ( s i n ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) − 1. ) ∗ ( s i n ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + 1. ) ) + 1.2 ∗ s q r t ( s i n ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + 1. ) ∗ s q r t ( s i n ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) − 1. ) ) ∗ ( 1. + s q r t ( 1 / ( ( s i n ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) − 1. ) ∗ ( s i n ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + 1. ) ) ) ∗ s q r t ( s i n ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) − 1. ) ∗ s q r t ( s i n ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + 1. ) ) / ( s q r t ( s i n ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + 1. ) ∗ s q r t ( s i n ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) − 1. ) ) ) ( 1 / 3 ) ) 2 {\displaystyle p[16]:=-1.0714+.71429*(-.50821*((1.1*ln(sin(1.3+1.4*x+1.5*t)+sqrt(sin(1.3+1.4*x+1.5*t)^{2}-1.))*sqrt((sin(1.3+1.4*x+1.5*t)-1.)*(sin(1.3+1.4*x+1.5*t)+1.))+1.2*sqrt(sin(1.3+1.4*x+1.5*t)+1.)*sqrt(sin(1.3+1.4*x+1.5*t)-1.))*(1.+sqrt(1/((sin(1.3+1.4*x+1.5*t)-1.)*(sin(1.3+1.4*x+1.5*t)+1.)))*sqrt(sin(1.3+1.4*x+1.5*t)-1.)*sqrt(sin(1.3+1.4*x+1.5*t)+1.))/(sqrt(sin(1.3+1.4*x+1.5*t)+1.)*sqrt(sin(1.3+1.4*x+1.5*t)-1.)))^{(}1/3)-(.88026*I)*((1.1*ln(sin(1.3+1.4*x+1.5*t)+sqrt(sin(1.3+1.4*x+1.5*t)^{2}-1.))*sqrt((sin(1.3+1.4*x+1.5*t)-1.)*(sin(1.3+1.4*x+1.5*t)+1.))+1.2*sqrt(sin(1.3+1.4*x+1.5*t)+1.)*sqrt(sin(1.3+1.4*x+1.5*t)-1.))*(1.+sqrt(1/((sin(1.3+1.4*x+1.5*t)-1.)*(sin(1.3+1.4*x+1.5*t)+1.)))*sqrt(sin(1.3+1.4*x+1.5*t)-1.)*sqrt(sin(1.3+1.4*x+1.5*t)+1.))/(sqrt(sin(1.3+1.4*x+1.5*t)+1.)*sqrt(sin(1.3+1.4*x+1.5*t)-1.)))^{(}1/3))^{2}} p [ 17 ] := − 1.0714 + .71429 ∗ ( − .50821 ∗ ( ( 1.1 ∗ l n ( s i n ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + s q r t ( s i n ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) 2 − 1. ) ) ∗ s q r t ( ( s i n ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) − 1. ) ∗ ( s i n ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + 1. ) ) + 1.2 ∗ s q r t ( s i n ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + 1. ) ∗ s q r t ( s i n ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) − 1. ) ) ∗ ( 1. + s q r t ( 1 / ( ( s i n ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) − 1. ) ∗ ( s i n ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + 1. ) ) ) ∗ s q r t ( s i n ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) − 1. ) ∗ s q r t ( s i n ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + 1. ) ) / ( s q r t ( s i n ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + 1. ) ∗ s q r t ( s i n ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) − 1. ) ) ) ( 1 / 3 ) + ( .88026 ∗ I ) ∗ ( ( 1.1 ∗ l n ( s i n ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + s q r t ( s i n ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) 2 − 1. ) ) ∗ s q r t ( ( s i n ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) − 1. ) ∗ ( s i n ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + 1. ) ) + 1.2 ∗ s q r t ( s i n ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + 1. ) ∗ s q r t ( s i n ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) − 1. ) ) ∗ ( 1. + s q r t ( 1 / ( ( s i n ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) − 1. ) ∗ ( s i n ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + 1. ) ) ) ∗ s q r t ( s i n ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) − 1. ) ∗ s q r t ( s i n ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + 1. ) ) / ( s q r t ( s i n ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + 1. ) ∗ s q r t ( s i n ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) − 1. ) ) ) ( 1 / 3 ) ) 2 {\displaystyle p[17]:=-1.0714+.71429*(-.50821*((1.1*ln(sin(1.3+1.4*x+1.5*t)+sqrt(sin(1.3+1.4*x+1.5*t)^{2}-1.))*sqrt((sin(1.3+1.4*x+1.5*t)-1.)*(sin(1.3+1.4*x+1.5*t)+1.))+1.2*sqrt(sin(1.3+1.4*x+1.5*t)+1.)*sqrt(sin(1.3+1.4*x+1.5*t)-1.))*(1.+sqrt(1/((sin(1.3+1.4*x+1.5*t)-1.)*(sin(1.3+1.4*x+1.5*t)+1.)))*sqrt(sin(1.3+1.4*x+1.5*t)-1.)*sqrt(sin(1.3+1.4*x+1.5*t)+1.))/(sqrt(sin(1.3+1.4*x+1.5*t)+1.)*sqrt(sin(1.3+1.4*x+1.5*t)-1.)))^{(}1/3)+(.88026*I)*((1.1*ln(sin(1.3+1.4*x+1.5*t)+sqrt(sin(1.3+1.4*x+1.5*t)^{2}-1.))*sqrt((sin(1.3+1.4*x+1.5*t)-1.)*(sin(1.3+1.4*x+1.5*t)+1.))+1.2*sqrt(sin(1.3+1.4*x+1.5*t)+1.)*sqrt(sin(1.3+1.4*x+1.5*t)-1.))*(1.+sqrt(1/((sin(1.3+1.4*x+1.5*t)-1.)*(sin(1.3+1.4*x+1.5*t)+1.)))*sqrt(sin(1.3+1.4*x+1.5*t)-1.)*sqrt(sin(1.3+1.4*x+1.5*t)+1.))/(sqrt(sin(1.3+1.4*x+1.5*t)+1.)*sqrt(sin(1.3+1.4*x+1.5*t)-1.)))^{(}1/3))^{2}} p [ 20 ] := − 1.0714 + .71429 ∗ ( − .64030 ∗ ( ( − 1.1 ∗ a r c t a n ( 1 / s q r t ( s e c ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) 2 − 1. ) ) ∗ s q r t ( s e c ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) − 1. ) ∗ s q r t ( s e c ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + 1. ) + 1.2 ∗ s q r t ( s e c ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) 2 − 1. ) ) / s q r t ( s e c ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) 2 − 1. ) ) ( 1 / 3 ) − ( 1.1091 ∗ I ) ∗ ( ( − 1.1 ∗ a r c t a n ( 1 / s q r t ( s e c ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) 2 − 1. ) ) ∗ s q r t ( s e c ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) − 1. ) ∗ s q r t ( s e c ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + 1. ) + 1.2 ∗ s q r t ( s e c ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) 2 − 1. ) ) / s q r t ( s e c ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) 2 − 1. ) ) ( 1 / 3 ) ) 2 {\displaystyle p[20]:=-1.0714+.71429*(-.64030*((-1.1*arctan(1/sqrt(sec(1.3+1.4*x+1.5*t)^{2}-1.))*sqrt(sec(1.3+1.4*x+1.5*t)-1.)*sqrt(sec(1.3+1.4*x+1.5*t)+1.)+1.2*sqrt(sec(1.3+1.4*x+1.5*t)^{2}-1.))/sqrt(sec(1.3+1.4*x+1.5*t)^{2}-1.))^{(}1/3)-(1.1091*I)*((-1.1*arctan(1/sqrt(sec(1.3+1.4*x+1.5*t)^{2}-1.))*sqrt(sec(1.3+1.4*x+1.5*t)-1.)*sqrt(sec(1.3+1.4*x+1.5*t)+1.)+1.2*sqrt(sec(1.3+1.4*x+1.5*t)^{2}-1.))/sqrt(sec(1.3+1.4*x+1.5*t)^{2}-1.))^{(}1/3))^{2}} p [ 21 ] := − 1.0714 + .71429 ∗ ( − .64030 ∗ ( ( − 1.1 ∗ a r c t a n ( 1 / s q r t ( s e c ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) 2 − 1. ) ) ∗ s q r t ( s e c ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) − 1. ) ∗ s q r t ( s e c ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + 1. ) + 1.2 ∗ s q r t ( s e c ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) 2 − 1. ) ) / s q r t ( s e c ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) 2 − 1. ) ) ( 1 / 3 ) + ( 1.1091 ∗ I ) ∗ ( ( − 1.1 ∗ a r c t a n ( 1 / s q r t ( s e c ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) 2 − 1. ) ) ∗ s q r t ( s e c ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) − 1. ) ∗ s q r t ( s e c ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + 1. ) + 1.2 ∗ s q r t ( s e c ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) 2 − 1. ) ) / s q r t ( s e c ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) 2 − 1. ) ) ( 1 / 3 ) ) 2 {\displaystyle p[21]:=-1.0714+.71429*(-.64030*((-1.1*arctan(1/sqrt(sec(1.3+1.4*x+1.5*t)^{2}-1.))*sqrt(sec(1.3+1.4*x+1.5*t)-1.)*sqrt(sec(1.3+1.4*x+1.5*t)+1.)+1.2*sqrt(sec(1.3+1.4*x+1.5*t)^{2}-1.))/sqrt(sec(1.3+1.4*x+1.5*t)^{2}-1.))^{(}1/3)+(1.1091*I)*((-1.1*arctan(1/sqrt(sec(1.3+1.4*x+1.5*t)^{2}-1.))*sqrt(sec(1.3+1.4*x+1.5*t)-1.)*sqrt(sec(1.3+1.4*x+1.5*t)+1.)+1.2*sqrt(sec(1.3+1.4*x+1.5*t)^{2}-1.))/sqrt(sec(1.3+1.4*x+1.5*t)^{2}-1.))^{(}1/3))^{2}} p [ 29 ] := − 1.0714 + .73794 ∗ ( ( 1.1 ∗ l n ( c o s ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + s q r t ( c o s ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) 2 − 1. ) ) ∗ s q r t ( ( c o s ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) − 1. ) ∗ ( c o s ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + 1. ) ) + 1.2 ∗ s q r t ( c o s ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + 1. ) ∗ s q r t ( c o s ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) − 1. ) ) ∗ ( 1. + s q r t ( 1 / ( ( c o s ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) − 1. ) ∗ ( c o s ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + 1. ) ) ) ∗ s q r t ( c o s ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) − 1. ) ∗ s q r t ( c o s ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + 1. ) ) / ( s q r t ( c o s ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + 1. ) ∗ s q r t ( c o s ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) − 1. ) ) ) ( 2 / 3 ) {\displaystyle p[29]:=-1.0714+.73794*((1.1*ln(cos(1.3+1.4*x+1.5*t)+sqrt(cos(1.3+1.4*x+1.5*t)^{2}-1.))*sqrt((cos(1.3+1.4*x+1.5*t)-1.)*(cos(1.3+1.4*x+1.5*t)+1.))+1.2*sqrt(cos(1.3+1.4*x+1.5*t)+1.)*sqrt(cos(1.3+1.4*x+1.5*t)-1.))*(1.+sqrt(1/((cos(1.3+1.4*x+1.5*t)-1.)*(cos(1.3+1.4*x+1.5*t)+1.)))*sqrt(cos(1.3+1.4*x+1.5*t)-1.)*sqrt(cos(1.3+1.4*x+1.5*t)+1.))/(sqrt(cos(1.3+1.4*x+1.5*t)+1.)*sqrt(cos(1.3+1.4*x+1.5*t)-1.)))^{(}2/3)} p [ 31 ] := − 1.0714 + .73794 ∗ ( ( 1.1 ∗ l n ( s i n ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + s q r t ( s i n ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) 2 − 1. ) ) ∗ s q r t ( ( s i n ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) − 1. ) ∗ ( s i n ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + 1. ) ) + 1.2 ∗ s q r t ( s i n ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + 1. ) ∗ s q r t ( s i n ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) − 1. ) ) ∗ ( 1. + s q r t ( 1 / ( ( s i n ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) − 1. ) ∗ ( s i n ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + 1. ) ) ) ∗ s q r t ( s i n ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) − 1. ) ∗ s q r t ( s i n ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + 1. ) ) / ( s q r t ( s i n ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + 1. ) ∗ s q r t ( s i n ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) − 1. ) ) ) ( 2 / 3 ) {\displaystyle p[31]:=-1.0714+.73794*((1.1*ln(sin(1.3+1.4*x+1.5*t)+sqrt(sin(1.3+1.4*x+1.5*t)^{2}-1.))*sqrt((sin(1.3+1.4*x+1.5*t)-1.)*(sin(1.3+1.4*x+1.5*t)+1.))+1.2*sqrt(sin(1.3+1.4*x+1.5*t)+1.)*sqrt(sin(1.3+1.4*x+1.5*t)-1.))*(1.+sqrt(1/((sin(1.3+1.4*x+1.5*t)-1.)*(sin(1.3+1.4*x+1.5*t)+1.)))*sqrt(sin(1.3+1.4*x+1.5*t)-1.)*sqrt(sin(1.3+1.4*x+1.5*t)+1.))/(sqrt(sin(1.3+1.4*x+1.5*t)+1.)*sqrt(sin(1.3+1.4*x+1.5*t)-1.)))^{(}2/3)} p [ 32 ] := − 1.0714 + 1.1714 ∗ ( ( − 1.1 ∗ a r c t a n ( 1 / s q r t ( c s c ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) 2 − 1. ) ) ∗ s q r t ( c s c ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) − 1. ) ∗ s q r t ( c s c ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + 1. ) + 1.2 ∗ s q r t ( c s c ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) 2 − 1. ) ) / s q r t ( c s c ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) 2 − 1. ) ) ( 2 / 3 ) {\displaystyle p[32]:=-1.0714+1.1714*((-1.1*arctan(1/sqrt(csc(1.3+1.4*x+1.5*t)^{2}-1.))*sqrt(csc(1.3+1.4*x+1.5*t)-1.)*sqrt(csc(1.3+1.4*x+1.5*t)+1.)+1.2*sqrt(csc(1.3+1.4*x+1.5*t)^{2}-1.))/sqrt(csc(1.3+1.4*x+1.5*t)^{2}-1.))^{(}2/3)} p [ 33 ] := − 1.0714 + 1.1714 ∗ ( ( − 1.1 ∗ a r c t a n ( 1 / s q r t ( s e c ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) 2 − 1. ) ) ∗ s q r t ( s e c ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) − 1. ) ∗ s q r t ( s e c ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + 1. ) + 1.2 ∗ s q r t ( s e c ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) 2 − 1. ) ) / s q r t ( s e c ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) 2 − 1. ) ) ( 2 / 3 ) {\displaystyle p[33]:=-1.0714+1.1714*((-1.1*arctan(1/sqrt(sec(1.3+1.4*x+1.5*t)^{2}-1.))*sqrt(sec(1.3+1.4*x+1.5*t)-1.)*sqrt(sec(1.3+1.4*x+1.5*t)+1.)+1.2*sqrt(sec(1.3+1.4*x+1.5*t)^{2}-1.))/sqrt(sec(1.3+1.4*x+1.5*t)^{2}-1.))^{(}2/3)} < p [ 34 ] := − 1.0714 + 1.1714 ∗ ( ( − 1.1 ∗ a r c t a n ( 1 / s q r t ( s e c h ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) 2 − 1. ) ) ∗ s q r t ( s e c h ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) − 1. ) ∗ s q r t ( s e c h ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) + 1. ) + 1.2 ∗ s q r t ( s e c h ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) 2 − 1. ) ) / s q r t ( s e c h ( 1.3 + 1.4 ∗ x + 1.5 ∗ t ) 2 − 1. ) ) ( 2 / 3 ) {\displaystyle <p[34]:=-1.0714+1.1714*((-1.1*arctan(1/sqrt(sech(1.3+1.4*x+1.5*t)^{2}-1.))*sqrt(sech(1.3+1.4*x+1.5*t)-1.)*sqrt(sech(1.3+1.4*x+1.5*t)+1.)+1.2*sqrt(sech(1.3+1.4*x+1.5*t)^{2}-1.))/sqrt(sech(1.3+1.4*x+1.5*t)^{2}-1.))^{(}2/3)} {\displaystyle } {\displaystyle } {\displaystyle } {\displaystyle } {\displaystyle } {\displaystyle } {\displaystyle } {\displaystyle } {\displaystyle } File:Hunter Saxton eq traveling wave plot 12.gif File:Hunter Saxton eq traveling wave plot 13.gif File:Hunter Saxton eq traveling wave plot 16.gif File:Hunter Saxton eq traveling wave plot 17.gif File:Hunter Saxton eq traveling wave plot 18.gif File:Hunter Saxton eq traveling wave plot 19.gif File:Hunter Saxton eq traveling wave plot 20.gif File:Hunter Saxton eq traveling wave plot 21.gif File:Hunter Saxton eq traveling wave plot 29.gif File:Hunter Saxton eq traveling wave plot 31.gif File:Hunter Saxton eq traveling wave plot 32.gif File:Hunter Saxton eq traveling wave plot 33.gif 雅可比橢圓函數展开 Hunter Saxton traveling wave Jacobi function plot 35.gif Jacobi function plot 35 Hunter Saxton traveling wave Jacobi function plot 36.gif Hunter Saxton traveling wave Jacobi function plot 41.gif Hunter Saxton traveling wave Jacobi function plot 43.gif Hunter Saxton traveling wave Jacobi function plot 46.gif Anders Samuelsen Nordli On the Hunter-Saxton equation，Norwegian University of Science and Technology，p38, June 2012 *谷超豪 《孤立子理论中的达布变换及其几何应用》 上海科学技术出版社 *阎振亚著 《复杂非线性波的构造性理论及其应用》 科学出版社 2007年 李志斌编著 《非线性数学物理方程的行波解》 科学出版社 王东明著 《消去法及其应用》 科学出版社 2002 *何青 王丽芬编著 《Maple 教程》 科学出版社 2010 ISBN 9787030177445 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 David Betounes, Partial Differential Equations for Computational Science: With Maple and Vector Analysis Springer, 1998 ISBN 9780387983004 George Articolo Partial Differential Equations & Boundary Value Problems with Maple V Academic Press 1998 ISBN 9780120644759 維基教科書中的相關電子教程：亨特 - 萨克斯顿方程