Nonlinear evolution equations have a major role in various scientific and engineering fields, such as fluid mechanics, plasma physics, optical fibers, solid state physics, chemical kinematics, chemical physics and geochemistry. Nonlinear wave phenomena of dispersion, dissipation, diffusion, reaction and convection are very important in nonlinear wave equations. In recent years, quite a few meth...

We study integrability of a system of nonlinear partial differential equations consisting of the nonlinear d’Alembert equation 2u = F (u) and nonlinear eikonal equation uxμuxμ = G(u) in the complex Minkowski space R(1, 3). A method suggested makes it possible to establish necessary and sufficient compatibility conditions and construct a general solution of the d’Alembert-eikonal system for all ...

this paper deals with the behavior at infinity of solutions to a class of wave equations with nonlinear dampingterms defined in a semi-infinite cylinder. the spatial behavior of solutions is studied and an alternative ofphragmén-lindelöf type theorems is obtained in the results. the main point in the contribution is the use of energy method.

New exact Grammian determinant solutions to two (3+1)-dimensional nonlinear evolution equations are derived. Extended set of sufficient conditions consisting of linear partial differential equations with variable-coefficients is presented. Moreover, a systematic analysis of linear partial differential equations is used for solving the representative linear systems. The bilinear Bäcklund transfo...