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We consider the equation      u t + u n u x + H ( x , t , u ) = 0 {u_t} + {u^n}{u_x} + H\left ( x, t, u \right ) = 0       and derive a transformation relating it to      u t + u n u x = 0 {u_t} + {u^n}{u_x} = 0       . Special cases of the equation appearing in applications are discussed. Initial value problems and asymptotic behaviour of the solution are studied.

On the solution of the equation 𝑢_{𝑡}+𝑢ⁿ𝑢ₓ+𝐻(𝑥,𝑡,𝑢)=0