12 research outputs found
Quasi self-adjoint nonlinear wave equations
In this paper we generalize the classification of self-adjoint second-order
linear partial differential equation to a family of nonlinear wave equations
with two independent variables. We find a class of quasi self-adjoint nonlinear
equations which includes the self-adjoint linear equations as a particular
case. The property of a differential equation to be quasi self-adjoint is
important, e.g. for constructing conservation laws associated with symmetries
of the differential equation
Self-adjointness and conservation laws of a generalized Burgers equation
A (2 + 1)-dimensional generalized Burgers equation is considered. Having
written this equation as a system of two dependent variables, we show that it
is quasi self-adjoint and find a nontrivial additional conservation law