Periodic solutions of hyperbolic partial differential equations

Periodic Solutions of Nonlinear Partial Differential Equations

As the existence theory for solutions of nonlinear partial differential equations becomes better understood, one can begin to ask more detailed questions about the behavior of solutions of such equations. Given the bewildering complexity which can arise from relatively simple systems of ordinary differential equations, it is hopeless to try to describe fully the behavior which might arise from ...

Periodic Solutions of Chaotic Partial Differential Equations

Hyperbolic Partial Differential Equations

Evolution equations associated with irreversible physical processes like diffusion and heat conduction lead to parabolic partial differential equations. When the equation is a model for a reversible physical process like propagation of acoustic or electromagnetic waves, then the evolution equation is generally hyperbolic. The mathematical models usually begin with a conservation statement that ...

Existence in the Large of Periodic Solutions of Hyperbolic Partial Differential Equations

where u = (u 1 . . . . , u.), and f = (fl . . . . . f . ) is periodic in x and y of period T, presents a number of difficulties when no damping of any sort is assumed. In this paper we analyze this difficult problem in the line of our previous work on ordinary and partial differential equations. We conclude with criteria of existence for solutions to the problem above. These criteria can then b...

Topological soliton solutions of the some nonlinear partial differential equations

In this paper, we obtained the 1-soliton solutions of the symmetric regularized long wave (SRLW) equation and the (3+1)-dimensional shallow water wave equations. Solitary wave ansatz method is used to carry out the integration of the equations and obtain topological soliton solutions The physical parameters in the soliton solutions are obtained as functions of the dependent coefficients. Note t...