We make an analysis of self-similar solutions for the mean curvature flow (MCF) by surfaces revolution and ruled in R3. prove that MCF non-cylindrical R3 are trivial. Moreover, we characterize revolutions under a homothetic helicoidal motion terms generating curve. Finally, cylindrical Explicit families exact also given.

For the most general supersymmetric solutions of type IIB supergravity consisting of a warped product of AdS5 with a five-dimensional manifold M5, we construct an explicit consistent Kaluza-Klein reduction on M5 to minimal D = 5 gauged supergravity. Thus, any solution of the gauged supergravity can be uplifted on M5 to obtain an exact solution of type IIB supergravity. We also show that for gen...

An explicit finite difference scheme for one-dimensional Burgers equation is derived from the lattice Boltzmannmethod. The system of the lattice Boltzmann equations for the distribution of the fictitious particles is rewritten as a three-level finite difference equation. The scheme is monotonic and satisfies maximum value principle; therefore, the stability is proved. Numerical solutions have b...

Using a complex representation of the Debney–Kerr–Schild (DKS) solutions and the Kerr theorem we analyze the boosted Kerr geometries and give the exact and explicit expressions for the metrics, the principal null congruences, the coordinate systems and the location of the singularities for arbitrary value and orientation of the boost with respect to the angular momentum. In the limiting, ultrar...

based on some stationary periodic solutions and stationary soliton solutions, one studies the general solution for the relative lax system, and a number of exact solutions to the korteweg-de vries (kdv) equation are first constructed by the known darboux transformation, these solutions include double and triple singular periodic solutions as well as singular soliton solutions whose amplitude de...

We present a methodology for characterization and an approach for computing the solutions of fuzzy linear systems with LR fuzzy variables. As solutions, notions of exact and approximate solutions are considered. We transform the fuzzy linear system into a corresponding linear crisp system and a constrained least squares problem. If the corresponding crisp system is incompatible, then the fuzzy ...

We comment on traveling wave solutions and rational solutions to the 3+1 dimensional Kadomtsev–Petviashvili (KP) equations: (ut + 6uux + uxxx)x ± 3uyy ± 3uzz = 0. We also show that both of the 3+1 dimensional KP equations do not possess the three-soliton solution. This suggests that none of the 3+1 dimensional KP equations should be integrable, and partially explains why they do not pass the Pa...