双重sinh-Gordon方程（Double sinh-Gordon equation）是一个非线性偏微分方程。.
u_{xt}=asinh(u)+bsinh(2u)
行波解
- {v = _C5JacobiCN(_C2+_C3x-(a_C5^2-2b_C5^2-2b-a)t/(_C3(_C5^2-1)), \sqrt((-2a_C5^2+a_C5^4+a+2b-2b_C5^4)(a_C5^2-2b_C5^2-a))_C5/(-2a_C5^2+a_C5^4+a+2b-2b*_C5^4))}
- {v = _C5JacobiDN(_C2+_C3x-_C5^2(a_C5^2-2b_C5^2-a)t/(_C3(-2_C5^2+1+_C5^4)), \sqrt((-2a_C5^2+a_C5^4+a+2b-2b_C5^4)(a_C5^2-2b_C5^2-a))/((a_C5^2-2b_C5^2-a)*_C5))}
- {v = _C5JacobiNC(_C2+_C3x+(a_C5^2-2b_C5^2-2b-a)t/(_C3(_C5^2-1)), \sqrt(-(-2a_C5^2+a_C5^4+a+2b-2b_C5^4)(a_C5^2-2b-a))/(-2a_C5^2+a_C5^4+a+2b-2b*_C5^4))}
- {v = _C5JacobiND(_C2+_C3x-(a_C5^2-2b-a)t/(_C3(-2_C5^2+1+_C5^4)), \sqrt(-(-2a_C5^2+a_C5^4+a+2b-2b_C5^4)(a_C5^2-2b-a))/(a_C5^2-2b-a))}
- {v = \sqrt(a(2b+a))csc(_C1+_C2x-(2b+a)t/_C2)/a}
- {v = \sqrt(a(2b+a))csc(_C2+_C3x-(2b+a)t/_C3)/a}
- {v = \sqrt(a(2b+a))sec(_C1+_C2x-(2b+a)t/_C2)/a}
- {v = \sqrt(a(2b+a))sech(_C1+_C2x+(2b+a)t/_C2)/a}
- {v = \sqrt(-a(2b+a))csch(_C1+_C2x+(2b+a)t/_C2)/a}
- {v = \sqrt((a-2b)a)cosh(_C2+_C3x-(a-2b)t/_C3)/(a-2*b)}
- {v = \sqrt((a-2b)(2b+a))tanh(_C1+_C2x+(1/8)(a^2-4b^2)t/(_C2b))/(a-2b)}
其中
v = tanh((1/2)*u)
特解
- u(x,t)= 2arctanh(1.5JacobiCN(1.2+1.3x+3.2307692307692307692*t, 1.0555973258234951998))
u(x,t)= 2arctanh(1.5JacobiDN(1.2+1.3x+3.6000000000000000000t, .94733093343134184593))
u(x,t)= 2arctanh(1.5JacobiNC(-1.2-1.3x+3.2307692307692307692t, .33806170189140663100I))
u(x,t)=2arctanh(1.5JacobiND(1.2+1.3x+.36923076923076923077t, 2.9580398915498080213I))
- u(x,t)=-2arctanh(\sqrt(3)csc(15.1-1.2x+2.5000000000000000000t))
- u(x,t)=-2arctanh(\sqrt(3)csc(-1.2-1.3x+2.3076923076923076923t))
- u(x,t)=2arctanh(\sqrt(3)sec(15.1-1.2x+2.5000000000000000000t))
- u(x,t)= 2arctanh(\sqrt(3)sech(-15.1+1.2x+2.5000000000000000000t))
- u(x,t)= 2arctanh(\sqrt(3)sech(1.2+1.3x+2.3076923076923076923t))
- u(x,t)= 2arctanh(\sqrt(-3)csch(-15.1+1.2x+2.5000000000000000000t))
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行波图
参考文献
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