Through assuming that nonlinear superposition principles NLSPs are embedded in a Lie group, a class of 3rd-order PDEs is derived from a general determining equation that determine the invariant group. The corresponding NLSPs and transformation to linearize the nonlinear PDE are found, hence the governing PDE is proved C-integrable. In the end, some applications of the PDEs are explained, which ...

The radiation and thermal diffusion effects on mixed convection flow of couple stress fluid through a channel are investigated. The governing non-linear partial differential equations are transformed into a system of ordinary differential equations using similarity transformations. The resulting equations are then solved using the Spectral Quasi-linearization Method (QLM). The results, which ar...

finding the most appropriate governing equation under different environmental conditions is the most important step for both designing sorption systems and pollutant transport modeling. in this study, the second order model based on the sorbent concentration is theoretically and experimentally investigated. a circular flume was used for the sorption of cadmium by zeolite to simulate the natural...

We analyze in classical L(R)-spaces, n = 2 or n = 3, 1 < q < ∞, a singular integral operator arising from the linearization of a hydrodynamical problem with a rotating obstacle. The corresponding system of partial differential equations of second order involves an angular derivative which is not subordinate to the Laplacian. The main tools are Littlewood– Paley theory and a decomposition of the...

In this paper we utilize the covariance of Riccati equation with respect to linear fractional transformations to define classes of conformally equivalent second order differential equations. This motivates then the introduction of fractional Darboux transformations which can be recognized also as generalized Cole-Hopf transformations. We apply these transformations to find Schrodinger equations...

In this article, we investigate a density problem coming from the linearization of Calderón’s problem with partial data. More precisely, we prove that the set of products of harmonic functions on a bounded smooth domain Ω vanishing on any fixed closed proper subset of the boundary are dense in L(Ω) in all dimensions n ≥ 2. This is proved using ideas coming from the proof of Kashiwara’s Watermel...

A method based on innnite parameter conservation laws is described to factor linear differential operators out of nonlinear partial diierential equations (PDEs) or out of diierential consequences of nonlinear PDEs. This includes a complete linearization to an equivalent linear PDE (system) if that is possible. Innnite parameter conservation laws can be computed, for example, with a computer alg...

Present study explores the effect of Hall current, non-linear radiation, irregular heat source/sink on magnetohydrodynamic flow of Casson nanofluid past a nonlinear stretching sheet. Viscous and Joule dissipation are incorporated in the energy equation. An accurate numerical solution of highly nonlinear partial differential equations, describing the flow, heat and mass transfer...

In industrial applications multi-channel data acquisition and logging is of prime importance for process monitoring and control. In such situations linearization of the non-linear responses obtained from multichannel data acquisition systems is of prime importance for precise monitoring and control. Although various techniques have been developed for sensor linearization, real time multi channe...