What does invariant exactly mean and how does it get the invariant?

Question

I have read many journal about simulation of regularized long wave. In numerical test section,many researcher use invariant of mass,momentum and energy to check accuracy of their method but i found there are different kind of the invariant that they've used.here example of invariant of energy. $$ I_3=\int_{a}^{b}u^3+3u^2\ dx $$ i get this equation from " Solitary Wave Solutions for the Regularized Long-Wave Equation " by D.Irk and this is another example. $$ I_3=\int_{a}^{b}u^4-3\mu u_x^2\ dx $$ this equation is taken from " A Numerical Solution of The Modified Regularized Long Wave (MRLW) Equation using Quartic B-Splines " by S. Battal Gazi Karakoc et al. so, how does it get the equations?