Separation Transformation and a Class of Exact Solutions to the Higher-Dimensional Klein-Gordon-Zakharov Equation

Table 1

Exact solutions of (𝑑𝑓(𝑤)/𝑑𝑤)²=𝑟+𝑞𝐹²+𝑝𝐹⁴(𝜔)(𝜔).

	𝑟	𝑞	𝑝	𝐹(𝜔)
1	1	−(1+𝑚^2)	𝑚^2	sn(𝜔,𝑚)
2	1−𝑚^2	2𝑚^2−1	−𝑚^2	cn(𝜔,𝑚)
3	𝑚^2−1	2−𝑚^2	−1	dn(𝜔,𝑚)
4	𝑚^2	−(1+𝑚^2)	1	𝑛𝑠(𝜔,𝑚)=[sn(𝜔,𝑚)]^−1
5	−𝑚^2	2𝑚^2−1	1−𝑚^2	𝑛𝑐(𝜔,𝑚)=[cn(𝜔,𝑚)]^−1
6	−1	2−𝑚^2	𝑚^2−1	𝑛𝑑(𝜔,𝑚)=[dn(𝜔,𝑚)]^−1
7	1	2−𝑚^2	1−𝑚^2	sc(𝜔,𝑚)=sn(𝜔,𝑚)/cn(𝜔,𝑚)
8	1	2𝑚^2−1	−𝑚^2(1−𝑚^2)	sd(𝜔,𝑚)=sn(𝜔,𝑚)/dn(𝜔,𝑚)
9	1−𝑚^2	2−𝑚^2	1	cs(𝜔,𝑚)=cn(𝜔,𝑚)/sn(𝜔,𝑚)
10	1	−(1+𝑚^2)	𝑚^2	cd(𝜔,𝑚)=cn(𝜔,𝑚)/dn(𝜔,𝑚)
11	−𝑚^2(1−𝑚^2)	2𝑚^2−1	1	ds(𝜔,𝑚)=dn(𝜔,𝑚)/sn(𝜔,𝑚)
12	𝑚^2	−(1+𝑚^2)	1	dc(𝜔,𝑚)=dn(𝜔,𝑚)/cn(𝜔,𝑚)
13	1/4	(1−2𝑚^2)/2	1/4	ns(𝜔,𝑚)+cs(𝜔,𝑚)
14	(1−𝑚^2)/4	(1+𝑚^2)/2	(1−𝑚^2)/4	nc(𝜔,𝑚)+sc(𝜔,𝑚)
15	𝑚^4/4	(𝑚^2−2)/2	1/4	ns(𝜔,𝑚)+ds(𝜔,𝑚)