In this article we prove an abstract Kolmogorov-Arnold-Moser (KAM) theorem for infinite dimensional reversible systems. Using theorem, obtain the existence of quasi-periodic solutions a class (non-Hamiltonian) coupled nonlinear Schrodinger systems on d-torus.

Estimating maximum scour depth is normally required in order to determine the depth of  bridge piles. The present paper uses the SSIIM Software which considers flow and sediment equations in a three dimensional manner. The software models flow field around circular bridge pile by resolving Navier-Stokes three-dimensional equations and k-  method, and by temporary solution of flow field and cont...

We propose a method to identify and classify evolution equations systems that can be multipotentialised in given target or systems. refer this as the {\it converse problem}. Although we mainly study for $(1+1)$-dimensional equations/system, do also an extension of methodology higher-dimensional equations. An important point is proposed allows one certain types auto-B\"acklund transformations eq...

two-dimensional euler equations have been solved on an unstructured grid. an upwind finite volume scheme, based on roes flux difference splitting method, is used to discretize the equations. using advancing front method, an initial delaunay triangulation has been made. the adaptation procedure involves mesh enrichment coarsening in regions of flow with high low gradients of flow properties, acc...

In this paper, a method for finding an approximate solution of a class of two-dimensional nonlinear Volterra integral equations of the first-kind is proposed. This problem is transformedto a nonlinear two-dimensional Volterra integral equation of the second-kind. The properties ofthe bivariate shifted Legendre functions are presented. The operational matrices of integrationtogether with the produ...

In this paper, we establish Lyapunov-type inequalities for a single higher-order differential equation, a cycled system and a coupled system with one-dimensional p -Laplacian. Our result generalize some given results.

We study an even dimensional manifold with a pseudo-Riemannian metric with arbitrary signature and arbitrary dimensions. We consider the Ricci flat equations and present a procedure to construct solutions to some higher (even) dimensional Ricci flat field equations from the four dimensional Ricci flat metrics. When the four dimensional Ricci flat geometry corresponds to a colliding gravitationa...