扎哈罗夫-库兹涅佐夫方程(Zhakharov-Kutznezov equation)是一个非线性偏微分方程[1]。
扎哈罗夫-库兹涅佐夫方程有许多解析解,包括[2]
![{\displaystyle u[4]:={\sqrt {(}}-a2/a[4])*sec({\sqrt {(}}-a2)*(l*\xi +m*\eta ))}](//wikimedia.org/api/rest_v1/media/math/render/svg/a37fa05488d35e58f4c4880db8fe32a70d4974dd)
![{\displaystyle u[5]:=e*{\sqrt {(}}a2/a4)*tan({\sqrt {(}}(1/2)*a2)*(l*\xi +m*\eta ))}](//wikimedia.org/api/rest_v1/media/math/render/svg/f0115027d722f3f001863c8f61ddc519858ccee3)
![{\displaystyle u[7]:=-a1/(2*a2)+e*a1*sinh(2*{\sqrt {(}}a2)*(l*\xi +m*\eta ))/(2*a2)}](//wikimedia.org/api/rest_v1/media/math/render/svg/9182d65ca035a0855112528532c446628b7ef221)
![{\displaystyle u[8]:=e*{\sqrt {(}}-a2/a4)*tanh({\sqrt {(}}-(1/2)*a2)*(l*\xi +m*\eta ))}](//wikimedia.org/api/rest_v1/media/math/render/svg/e3423882e86181d2bf4c2421211ed015f87388d4)
![{\displaystyle u[9]:=-a2*sech({\sqrt {(}}(1/2)*a2)*(l*\xi +m*\eta ))^{2}/a3}](//wikimedia.org/api/rest_v1/media/math/render/svg/cd1b616b32d4e41cd177238a4ebe1c0e5a2e71c0)
![{\displaystyle u[11]:=1/(a3*(l*\xi +m*\eta )^{2})}](//wikimedia.org/api/rest_v1/media/math/render/svg/7fcc2d29b58f4e3d6ac83652cfac52ab23addcfd)
其中
参数:params := a1 = 1, a2 = 1, a3 = 2.3, a4 = 3.4, d = 1.2, e = 1.3, m = 5.35, c[1] = 5.22, c[2] = 3.23, c[3] = 1.3, c3 = 3.33, c[4] = 1.35, c4 = 1.44, l = 2.1, a[1] = 3.1, a[2] = 3.23, a0 = 5.34, a = .7, c = 1.1;
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Zakharov-Kutznezov equation plot1
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Zakharov-Kutznezov equation plot4
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Zakharov-Kutznezov equation plot5
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Zakharov-Kutznezov equation plot7
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Zakharov-Kutznezov equation plot8
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Zakharov-Kutznezov equation plot9
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Zakharov-Kutznezov equation plot11
Touqeer Nawaza,
Ahmet Yıldırımb, Syed Tauseef Mohyud-Din:Analytical solutions Zakharov–Kuznetsov equations,Advanced Powder Technology,Volume 24, Issue 1, January 2013, Pages 252–256
YAN Zhi-Lian and LIU Xi-Qiang Symmetry Reductions and Explicit Solutions for a Generalized Zakharov Kuznetsov Equation,Commun. Theor. Phys. (Beijing, China) 45 (2006) pp. 29–32
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