Self-Adjointness, Symmetries, and Conservation Laws for a Class of Wave Equations Incorporating Dissipation

Table 2

Symmetries of (3) for some special choices of 𝑓 and 𝑔.

𝑓	𝑔	Symmetries
𝑢^−2	ln𝑢	𝑋3𝜕=𝑥𝜕𝜕𝑥−𝑢𝜕𝑢
𝑢^𝑛 (𝑛≠0)	1	𝑋3𝜕=𝑥+𝜕𝑥2𝑢𝑛𝜕𝜕𝑢
1	𝑢	𝑋3𝜕=𝑢𝜕𝑢, 𝑋4𝜕=𝑡𝜕𝜕𝑥+𝑥−1𝜕𝑡2𝜕(𝑡+𝛼𝑥)𝑢𝜕𝑢
1	1	𝑋3𝜕=𝑢𝜕𝑢, 𝑋4𝜕=𝑡𝜕𝜕𝑥+𝑥−1𝜕𝑡2𝜕𝛼𝑥𝑢𝜕𝑢