A Class Of Second Order With Variable Coefficients Nonlinear Partial Differential Equations B (?) Backlund Transformation Of The Classification,

In this paper we classify B?cklund transformations u v for the second-order variable coefficients partial differential equations of the form defined via associated integrable systems of the form We show that such a nonlinear partial differential equation is equivalent to the Burgers equation and the associated integrable system takes the following two forms: whereλis an arbitrary constant; or with c₁ , c₂being arbitrary constants.As an application, by applying the above second Backlund transformation to the solution of the Burgers equation we obtain a new solution of the Burgers equation: whereλis an arbitrary constant; and applying the B?cklund transformation to u1 (x,t) yields the following solution of the Burgers equation where c1 ,λ2are arbitrary constants.If applying the second B?cklund transformation to the trivial solution of the Burgers equation, we get an interesting new solution of the Burgers equation...