The Expansions Of Conservation Laws And Symmetries For A PDE(s) And Applications Of Differential Form Wu's Method

Firstly, using strategy of introducing associated auxiliary equation(s) to a givenpartial differential equation(s) without admitting Lagrangian, we make the extendedequations possess a variational principle. Based on this, the concepts of extendedconservation law and extended symmetry to given partial differential equation(s)are put forwarded. Secondly, A computational method to produce extended sym-metries and extended conservation laws to given partial differential equation(s) aresuggested. Thirdly, an algorithm to determine original conservation laws of generalform partial differential equation(s) is given. Fourthly, in our methods the differ-ential form Wu's method is used to solve the system of determining equations forconservation laws and symmetries of given equation(s). Finally, as applications ofour methods given in this paper, new (extended) conservation laws and symmetriesfor five evolution equations included nonlinear Telegraph equations are determined.The validity of the method are explained at the same time.