<p style='text-indent:20px;'>We consider a damped Klein-Gordon equation with variable diffusion coefficient. This problem is challenging because of the equation's unbounded nonlinearity. First, we study nonlinearity's continuity properties. Then existence and uniqueness solutions established. The main result solution map on set admissible parameters. Its application to parameter identific...

An useful strategy for the study of nonlinear partial differential equations (PDE) arising in pattern formation is to consider asymptotic solutions containing one or several localized defects and to simplify the dynamics by finding the equations of motion of the system of interacting defects. The great advantage of this approach is that we are dealing with ordinary differential equations (ODEs)...

A new transformation method is developed using the general sine-Gordon travelling wave reduction equation and a generalized transformation. With the aid of symbolic computation, this method can be used to seek more types of solutions of nonlinear differential equations, which include not only the known solutions derived by some known methods but new solutions. Here we choose the double sine-Gor...