Higher-dimensional integrable systems from multilinear evolution equations

Higher-Dimensional Integrable Systems from Multilinear Evolution Equations

A multilinear M -dimensional generalization of Lax pairs is introduced and its explicit form is given for the recently discovered class of time-harmonic, integrable, hypersurface motions in IR.

Integrable Cosmological Models From Higher Dimensional Einstein Equations

We consider the cosmological models for the higher dimensional spacetime which includes the curvatures of our space as well as the curvatures of the internal space. We find that the condition for the integrability of the cosmological equations is that the total space-time dimensions are D = 10 or D = 11 which is exactly the conditions for superstrings or M-theory. We obtain analytic solutions w...

Exact solutions of (3 +1)-dimensional nonlinear evolution equations

In this paper, the kudryashov method has been used for finding the general exact solutions of nonlinear evolution equations that namely the (3 + 1)-dimensional Jimbo-Miwa equation and the (3 + 1)-dimensional potential YTSF equation, when the simplest equation is the equation of Riccati.

Integrable geometric evolution equations for curves

The vortex filament flow and planar filament flow are examples of evolution equations which commute with Euclidean isometries and are also integrable, in that they induce completely integrable PDE for curvature—the focusing nonlinear Schödinger equation and the mKdV equations, respectively. In this note we outline an approach for classifying integrable geometric evolution equations for planar c...

Integrable Evolution Equations in Time-Dependent Domains