Kink Solutions for a Class of Generalized Dissipative Equations

Table 1

Group classification of (1.1). 𝑓₀, 𝜆₀, 𝑝, 𝑞, 𝑟, and 𝑠 are constitutive constants with 𝑓₀, 𝜆₀>0, and 𝑝, 𝑠≠0.

Case	𝑓(𝑢) and 𝜆(𝑢)	Extensions of ℒ𝒫
I	𝑓=𝑓0𝑒^𝑢/𝑝, 𝜆=𝜆0𝑒^𝑢/𝑠	𝑋3𝑡𝜕=2𝑠−𝑝+𝑥𝜕𝜕𝑡𝑠−2𝑝𝜕𝜕𝑥−2𝑝𝑠𝜕𝑢
II	𝑓=𝑓0𝑢+𝑞^1/𝑝, 𝜆=𝜆0𝑢+𝑞^(1+𝑟)/𝑝	𝑋3𝜕=2𝑟𝑡+()𝑥𝜕𝜕𝑡1+2𝑟𝜕𝜕𝑥+2𝑝𝑢+𝑞𝜕𝑢
III	𝑓=𝑓0𝑢+𝑞^−4/3, 𝜆=𝜆0𝑢+𝑞^−4/3	𝑋3𝜕=𝑥−3𝜕𝑥2𝜕𝑢+𝑞𝜕𝑢
		𝑋4=𝑥^2𝜕𝜕𝜕𝑥−3𝑥𝑢+𝑞𝜕𝑢