The Generation of Formal Conservation Law of Evolution Equations - Adji, Teguh Bharata (2010)
Many evolution equations such as the soliton (solitary equation) of Korteweg-de Vries (KdV) equation have been found recently to have various kinds of explicit integral or solutions. Such evolution equations admit infinitely many conservation laws or admit symplectic operators. This research uses the definition of the formal conservation law, which is the approximation of the symplectic operator. This formal conservation law definition provides a convenient way to characterizing equations admitting infinitely many conservation laws. A program for computing the formal conservation law of evolution equations was developed. The program was then verified with some evolution equations as testing equations, which have been proved to be formally completely integrable. The developed program can compute the formal conservation law of finite arbitrary order (up to order 18) of the testing equations.