Conservation laws of KdV equation with time dependent coefficients

We determine conservation laws of the generalized KdV equation of time dependent variable coefficients of the linear damping and dispersion. The underlying equation is not derivable from a variational principle and hence one cannot use Noether’s theorem here to construct conservation laws as there is no Lagrangian. However, we show that by utilizing the new conservation theorem and the partial Lagrangian approach one can construct a number of local and nonlocal conservation laws for the underlying equation.

Research highlights
► Conservation laws of the generalized KdV equation of variable coefficients are obtained.
► The equation does not have a Lagrangian hence one cannot use Noethera’s theorem.
► We utilize the new conservation theorem and the partia Lagrangian approach to construct conservation laws.