双重sinh-Gordon方程

双重sinh-Gordon方程（Double sinh-Gordon equation）是一个非线性偏微分方程。^[1]^[2]^[3]^[4]^[5].

$u_{x t} = a s i n h (u) + b s i n h (2 u)$

行波解

$v =_{C} 5 * J a c o b i C N (_{C} 2 +_{C} 3 * x - (a *_{C} 5^{2} - 2 * b *_{C} 5^{2} - 2 * b - a) * t / (_{C} 3 * (_{C} 5^{2} - 1)), \sqrt{(} (- 2 * a *_{C} 5^{2} + a *_{C} 5^{4} + a + 2 * b - 2 * b *_{C} 5^{4}) * (a *_{C} 5^{2} - 2 * b *_{C} 5^{2} - a)) *_{C} 5 / (- 2 * a *_{C} 5^{2} + a *_{C} 5^{4} + a + 2 * b - 2 * b *_{C} 5^{4}))$
$v =_{C} 5 * J a c o b i D N (_{C} 2 +_{C} 3 * x -_{C} 5^{2} * (a *_{C} 5^{2} - 2 * b *_{C} 5^{2} - a) * t / (_{C} 3 * (- 2 *_{C} 5^{2} + 1 +_{C} 5^{4})), \sqrt{(} (- 2 * a *_{C} 5^{2} + a *_{C} 5^{4} + a + 2 * b - 2 * b *_{C} 5^{4}) * (a *_{C} 5^{2} - 2 * b *_{C} 5^{2} - a)) / ((a *_{C} 5^{2} - 2 * b *_{C} 5^{2} - a) *_{C} 5))$
$v =_{C} 5 * J a c o b i N C (_{C} 2 +_{C} 3 * x + (a *_{C} 5^{2} - 2 * b *_{C} 5^{2} - 2 * b - a) * t / (_{C} 3 * (_{C} 5^{2} - 1)), \sqrt{(} - (- 2 * a *_{C} 5^{2} + a *_{C} 5^{4} + a + 2 * b - 2 * b *_{C} 5^{4}) * (a *_{C} 5^{2} - 2 * b - a)) / (- 2 * a *_{C} 5^{2} + a *_{C} 5^{4} + a + 2 * b - 2 * b *_{C} 5^{4}))$
$v =_{C} 5 * J a c o b i N D (_{C} 2 +_{C} 3 * x - (a *_{C} 5^{2} - 2 * b - a) * t / (_{C} 3 * (- 2 *_{C} 5^{2} + 1 +_{C} 5^{4})), \sqrt{(} - (- 2 * a *_{C} 5^{2} + a *_{C} 5^{4} + a + 2 * b - 2 * b *_{C} 5^{4}) * (a *_{C} 5^{2} - 2 * b - a)) / (a *_{C} 5^{2} - 2 * b - a))$
$v = \sqrt{(} a * (2 * b + a)) * c s c (_{C} 1 +_{C} 2 * x - (2 * b + a) * t /_{C} 2) / a$
$v = \sqrt{(} a * (2 * b + a)) * c s c (_{C} 2 +_{C} 3 * x - (2 * b + a) * t /_{C} 3) / a$
$v = \sqrt{(} a * (2 * b + a)) * s e c (_{C} 1 +_{C} 2 * x - (2 * b + a) * t /_{C} 2) / a$
$v = \sqrt{(} a * (2 * b + a)) * s e c h (_{C} 1 +_{C} 2 * x + (2 * b + a) * t /_{C} 2) / a$
$v = \sqrt{(} - a * (2 * b + a)) * c s c h (_{C} 1 +_{C} 2 * x + (2 * b + a) * t /_{C} 2) / a$
$v = \sqrt{(} (a - 2 * b) * a) * c o s h (_{C} 2 +_{C} 3 * x - (a - 2 * b) * t /_{C} 3) / (a - 2 * b)$
$v = \sqrt{(} (a - 2 * b) * (2 * b + a)) * t a n h (_{C} 1 +_{C} 2 * x + (1 / 8) * (a^{2} - 4 * b^{2}) * t / (_{C} 2 * b)) / (a - 2 * b)$

其中 $v = t a n h ((1 / 2) * u)$

特解

$u (x, t) = 2 a r c t a n h (1.5 * J a c o b i C N (1.2 + 1.3 * x + 3.2307692307692307692 * t, 1.0555973258234951998))$
$u (x, t) = 2 a r c t a n h (1.5 * J a c o b i D N (1.2 + 1.3 * x + 3.6000000000000000000 * t, . 94733093343134184593))$
$u (x, t) = 2 * a r c t a n h (1.5 * J a c o b i N C (- 1.2 - 1.3 * x + 3.2307692307692307692 * t, . 33806170189140663100 * I))$
$u (x, t) = 2 * a r c t a n h (1.5 * J a c o b i N D (1.2 + 1.3 * x + . 36923076923076923077 * t, 2.9580398915498080213 * I))$
$u (x, t) = - 2 * a r c t a n h (\sqrt{(} 3) * c s c (15.1 - 1.2 * x + 2.5000000000000000000 * t))$
$u (x, t) = - 2 * a r c t a n h (\sqrt{(} 3) * c s c (- 1.2 - 1.3 * x + 2.3076923076923076923 * t))$
$u (x, t) = 2 * a r c t a n h (\sqrt{(} 3) * s e c (15.1 - 1.2 * x + 2.5000000000000000000 * t))$
$u (x, t) = 2 * a r c t a n h (\sqrt{(} 3) * s e c h (- 15.1 + 1.2 * x + 2.5000000000000000000 * t))$
$u (x, t) = 2 * a r c t a n h (\sqrt{(} 3) * s e c h (1.2 + 1.3 * x + 2.3076923076923076923 * t))$
$u (x, t) = 2 * a r c t a n h (\sqrt{(} - 3) * c s c h (- 15.1 + 1.2 * x + 2.5000000000000000000 * t))$

行波图

参考文献

↑ Andrei D. Polyanin, Valentin F. Zaitsev, HANDBOOK OF NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS SECOND EDITION CRC Press, A Chapman & Hall Book ISBN 9781420087239
↑ Zeitschrift Für Naturforschung: A journal of physical sciences 2004 p933-937
↑ A. M. WAZWAZ Exact solutions to the double sinh-gordon equation by the tanh method and a variable separated ODE method,Computers & Mathematics with Applications,Volume 50, Issues 10–12, November–December 2005, Pages 1685–1696
↑ Issues in Logic, Operations, and Computational Mathematics and Geometry 2013 p484
↑ Mathematical Reviews - Page 3708 2007

[1] Andrei D. Polyanin, Valentin F. Zaitsev, HANDBOOK OF NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS SECOND EDITION CRC Press, A Chapman & Hall Book ISBN 9781420087239

[2] Zeitschrift Für Naturforschung: A journal of physical sciences 2004 p933-937

[3] A. M. WAZWAZ Exact solutions to the double sinh-gordon equation by the tanh method and a variable separated ODE method,Computers & Mathematics with Applications,Volume 50, Issues 10–12, November–December 2005, Pages 1685–1696

[4] Issues in Logic, Operations, and Computational Mathematics and Geometry 2013 p484

[5] Mathematical Reviews - Page 3708 2007

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双重sinh-Gordon方程

目录

行波解

特解

行波图

参考文献

导航菜单

双重sinh-Gordon方程

行波解

特解

行波图

参考文献

导航菜单

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