Systematic construction of infinitely many conservation laws for certain nonlinear evolution equations in mathematical physics

Conservation law plays a vital role in the study of nonlinear evolution equations, particularly with regard to integrability, linearization and constants of motion. In the present paper, it is shown that infinitely many conservation laws for certain nonlinear evolution equations are systematically constructed with symbolic computation in a simple way from the Riccati form of the Lax pair. Note that the Lax pairs investigated here are associated with different linear systems, including the generalized Kaup–Newell (KN) spectral problem, the generalized Ablowitz–Kaup–Newell–Segur (AKNS) spectral problem, the generalized AKNS–KN spectral problem and a recently proposed integrable system. Therefore, the power and efficiency of this systematic method is well understood, and we expect it may be useful for other nonlinear evolution models, even higher-order and variable-coefficient ones.

► Infinitely many conservation laws for certain nonlinear evolution equations are systematically constructed.
► Riccati-equation-method of the associated Lax pair is used.
► The Lax pairs investigated here belong to different generalized linear systems.
► Calculations here are manipulated with computerized symbolic computation.