Conditional Lie-Bäcklund Symmetries and Reductions of the Nonlinear Diffusion Equations with Source

Table 3

CLBS (15) and IS (19) with 𝑙=3,4 of (14).

Number	Equation (14)	CLBS (15)	IS (19)
1	𝑣𝑡=2𝑒^(𝑝−𝑞)𝑥𝑣𝑥𝑣𝑥𝑥+𝑝2𝑣𝑥+𝛼𝑣+𝛽+𝛾𝑒^−(𝑝/2)𝑥+𝜆𝑓2^(16)(𝑥)^2	𝜂=𝑣𝑥𝑥𝑥+3𝑝−2𝑞2𝑣𝑥𝑥+𝑝^2−𝑝𝑞2𝑣𝑥	𝑊𝑒^−(𝑝/2)𝑥,(𝑓2^(16)(𝑥))^2,1
2	𝑣𝑡=2𝑒^(𝑝−𝑞)𝑥𝑣𝑥𝑣𝑥𝑥+𝑝2𝑣𝑥+𝛼𝑣+𝛽+𝛾𝑓2^(16)(𝑥)^2+𝜆𝑓2^(16)(𝑥)	𝜂=𝑣𝑥𝑥𝑥+3𝑝−3𝑞2𝑣𝑥𝑥+(𝑝−𝑞)^22𝑣𝑥	𝑊(𝑓2^(14)(𝑥))^2,𝑓2^(16)(𝑥),1
3	𝑣𝑡=2𝑒^(𝑝−𝑞)𝑥𝑣𝑥𝑣𝑥𝑥+𝑝2𝑣𝑥−𝑝−𝑞(3𝑝−4𝑞)^2𝑣^2𝑒^(𝑝−𝑞)𝑥+𝛼𝑣+𝛽𝑒^−(𝑝−𝑞)𝑥+𝛾𝑓2^(17)(𝑥)+𝜆𝑓3^(17)(𝑥)	𝜂=𝑣𝑥𝑥𝑥+3𝑝−𝑞𝑣𝑥𝑥+5𝑝−6𝑞(𝑝−𝑞)𝑣𝑥+3𝑝−4𝑞(𝑝−𝑞)^2𝑣	𝑊𝑒^−(𝑝−𝑞)𝑥,𝑓2^(17)(𝑥),𝑓3^(17)(𝑥)
4	𝑣𝑡=2𝑒^(𝑝−𝑞)𝑥𝑣𝑥𝑣𝑥𝑥+𝑝2𝑣𝑥−11253𝑝−2𝑞(𝑝+𝑞)^2𝑣^2𝑒^(𝑝−𝑞)𝑥+𝛼𝑣+𝛽𝑓1^(18)(𝑥)+𝛾𝑓2^(18)(𝑥)+𝜆𝑓3^(18)(𝑥)	𝜂=𝑣𝑥𝑥𝑥+9𝑝−6𝑞5𝑣𝑥𝑥+23𝑝^2−24𝑝𝑞+3𝑞^2𝑣25^𝑥+1𝑣25𝑝−𝑞3𝑝−2𝑞𝑝+𝑞	𝑊𝑓1^(18)(𝑥),𝑓2^(18)(𝑥),𝑓3^(18)(𝑥)
5	𝑣𝑡=2𝑒^(4𝑝/5)𝑥𝑣𝑥𝑣𝑥𝑥+𝑝2𝑣𝑥+𝛼𝑣+𝛽+𝛾𝑒^−(2𝑝/5)𝑥+𝜆𝑒^−(3𝑝/5)𝑥	𝜂=𝑣𝑥𝑥𝑥+𝑝𝑣𝑥𝑥+6𝑝^2𝑣25^𝑥	𝑊𝑒^−(2𝑝/5)𝑥,𝑒^−(3𝑝/5)𝑥,1
6	𝑣𝑡=𝑒^(3𝑝/2)𝑥−2𝑣𝑣𝑥𝑣𝑥𝑥+𝑝2𝑣𝑥+𝑣^3𝑥−𝛼𝑣+𝛽+𝛾𝑒^−(𝑝/2)𝑥+𝜆𝑒^−𝑝𝑥	𝜂=𝑣𝑥𝑥𝑥+3𝑝2𝑣𝑥𝑥+𝑝^22𝑣𝑥	𝑊𝑒^−(𝑝/2)𝑥,𝑒^−𝑝𝑥,1
7	𝑣𝑡=2𝑒^(3𝑝/2)𝑥𝑣𝑥𝑣𝑥𝑥+𝑝2𝑣𝑥+𝛼𝑣+𝛽+𝛾𝑒^−(𝑝/2)𝑥+𝜆𝑒^−𝑝𝑥	𝜂=𝑣𝑥𝑥𝑥+3𝑝2𝑣𝑥𝑥+𝑝^22𝑣𝑥	𝑊𝑒^−(𝑝/2)𝑥,𝑒^−𝑝𝑥,1
8	𝑣𝑡=3𝑒^(𝑝/2)𝑥𝑣^2𝑥𝑣𝑥𝑥+𝑝3𝑣𝑥+𝛼𝑣+𝛽+𝛾𝑒^−(𝑝/3)𝑥+𝜆𝑒^−(𝑝/6)𝑥	𝜂=𝑣𝑥𝑥𝑥+𝑝2𝑣𝑥𝑥+𝑝^2𝑣18^𝑥	𝑊𝑒^−(𝑝/3)𝑥,𝑒^−(𝑝/6)𝑥,1
9	𝑣𝑡=3𝑒^(4𝑝/3)𝑥𝑣^2𝑥𝑣𝑥𝑥+𝑝3𝑣𝑥+𝛼𝑣+𝛽+𝛾𝑒^−(𝑝/3)𝑥+𝜆𝑒^−(2𝑝/3)𝑥	𝜂=𝑣𝑥𝑥𝑥+𝑝𝑣𝑥𝑥+2𝑝^29𝑣𝑥	𝑊𝑒^−(𝑝/3)𝑥,𝑒^−(2𝑝/3)𝑥,1
10	𝑣𝑡=𝑒^(4𝑝/3)𝑥274𝑣𝑣^2𝑥𝑣𝑥𝑥+𝑝3𝑣𝑥−278𝑣^4𝑥−23𝛼𝑣+𝛽+𝛾𝑒^−(𝑝/3)𝑥𝜆𝑒^−(2𝑝/3)𝑥	𝜂=𝑣𝑥𝑥𝑥+𝑝𝑣𝑥𝑥+2𝑝^29𝑣𝑥	𝑊𝑒^−(𝑝/3)𝑥,𝑒^−(2𝑝/3)𝑥,1
11	𝑣𝑡=3𝑒^(6𝑝/7)𝑥𝑣^2𝑥𝑣𝑥𝑥+𝑝3𝑣𝑥+𝛼𝑣+𝛽+𝛾𝑒^−(2𝑝/7)𝑥+𝜆𝑒^−(5𝑝/7)𝑥	𝜂=𝑣𝑥𝑥𝑥+5𝑝7𝑣𝑥𝑥+6𝑝^2𝑣49^𝑥	𝑊𝑒^−(2𝑝/7)𝑥,𝑒^−(5𝑝/7)𝑥,1
12	𝑣𝑡=2𝑒^(3𝑝/2)𝑥𝑣𝑥𝑣𝑥𝑥+𝑝2𝑣𝑥+𝛼𝑣+𝛽+𝛾𝑒^−𝑝𝑥+𝜆𝑒^−(𝑝/2)𝑥+𝜇𝑒^−(𝑝/3)𝑥	𝜂=𝑣𝑥𝑥𝑥𝑥+3𝑝𝑣𝑥𝑥𝑥+11𝑝^24𝑣𝑥𝑥+3𝑝^34𝑣𝑥	𝑊𝑒^−𝑝𝑥,𝑒^−(𝑝/2)𝑥,𝑒^−(𝑝/3)𝑥,1
13	𝑣𝑡=2𝑒^(𝑝/3)𝑥𝑣𝑥𝑣𝑥𝑥+𝑝2𝑣𝑥+𝛼𝑣+𝛽+𝛾𝑒^−(𝑝/2)𝑥+𝜆𝑒^−(𝑝/3)𝑥+𝜇𝑒^−(𝑝/6)𝑥	𝜂=𝑣𝑥𝑥𝑥𝑥+𝑝𝑣𝑥𝑥𝑥+11𝑝^2𝑣36^𝑥𝑥+𝑝^3𝑣36^𝑥	𝑊𝑒^−(𝑝/2)𝑥,𝑒^−(𝑝/3)𝑥,𝑒^−(𝑝/6)𝑥,+1
14	𝑣𝑡=2𝑒^(4𝑝/5)𝑥𝑣𝑥𝑣𝑥𝑥+𝑝2𝑣𝑥+𝛼𝑣+𝛽+𝛾𝑒^−(2𝑝/5)𝑥+𝜆𝑒^−(3𝑝/5)𝑥+𝜇𝑒^−(4𝑝/5)𝑥	𝜂=𝑣𝑥𝑥𝑥𝑥+9𝑝5𝑣𝑥𝑥𝑥+26𝑝^2𝑣25^𝑥𝑥+24𝑝^3𝑣125^𝑥	𝑊𝑒^−(2𝑝/5)𝑥,𝑒^−(3𝑝/5)𝑥,𝑒^−(4𝑝/5)𝑥,1