Conservation laws of inviscid Burgers equation with nonlinear damping

•Many conservations laws of damped inviscid Burgers equation were exhibited.•We establish conditions for quasi self-adjoint and self-adjoint of equation considered.•The quasi self-adjoint and self-adjoint conditions were used to simplify conserved quantities.•The conservation laws for the quasi self-adjoint case found are infinite.

In this paper, the new conservation theorem presented in Ibragimov (2007) [14] is used to find conservation laws of the inviscid Burgers equation with nonlinear damping ut+g(u)ux+λh(u)=0ut+g(u)ux+λh(u)=0. We show that this equation is both quasi self-adjoint and self-adjoint, and use these concepts to simplify conserved quantities for various choices of g(u)g(u) and h(u)h(u).