Conservation Laws Of KdV Equation Research Articles

Nonlinear Self-Adjointness and Conservation Laws of KdV Equation with Linear Damping Force

Nonlinear Self-Adjointness and Conservation Laws of KdV Equation with Linear Damping Force

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.

Appell’s lemma and conservation laws of KdV equation

An alternative method to construct a class of conservation laws of the KdV equation based on the classical Appell’s lemma and the trace formulas of Deift–Trubowitz type is studied. A new type of infinite sequence of conservation laws whose local densities cannot be expressed in terms of differential polynomials is constructed.