Taking the example of Koretweg–de Vries equation, it is shown that soliton solutions need not always be the consequence of the trade-off between the nonlinear terms and the dispersive term in the nonlinear differential equation. Even the ordinary one dimensional linear partial differential equation can produce a soliton. Solitary waves and solitons are often described [1-8] as a consequence of ...

We present and analyse a novel manifestation of the revival phenomenon for linear spatially periodic evolution equations, in concrete case three nonlocal equations that arise water wave theory are defined by convolution kernels. Revival these cases is manifested form dispersively quantised cusped solutions at rational times. give an analytic description this phenomenon, illustrative numerical s...

We study an integrable model of one-dimensional strongly correlated electrons at finite temperature by explicit calculation of the correlation lengths of various correlation functions. The model is invariant with respect to the quantum superalgebra Uq(sl(2|1)) and characterized by the Hubbard interaction, correlated hopping and pair-hopping terms. Using the integrability, the graded quantum tra...

The study is financially supported by the National Natural Science Foundation of China (50979036), and by the Foundation of National Water Pollution Control and Governance of China (NO. 2009ZX07210007-01). Abstract—In the calculation of mixed-transport capacity of pollutants which were discharged from bank outfall of wide straight rivers or reservoirs, the lateral diffusion coefficient can bett...

This work reports new approaches for order reduction of nonlinear systems with time periodic coefficients. First, the equations of motion are transformed using the Lyapunov-Floquet (LF) transformation, which makes the linear part of new set of equations time invariant. At this point, either linear or nonlinear order reduction methodologies can be applied. The linear order reduction technique is...

‎the problem of two-phase mhd boundary layer flow, heat and mass transfer over a stretching sheet with fluid-particle suspension and thermal radiation has been studied. the effect of mass transfer in dusty fluid over a stretching sheet is considered for the first time. the governing equations are reduced to a set of non-linear ordinary differential equations under suitable similarity transforma...

Advances in the visualization and prediction of turbulence are shedding new light on mass transfer in the turbulent boundary layer. These discoveries have important implications for many topics in environmental science and engineering, from the transport of earth-warming CO2 across the sea-air interface, to nutrient processing and sediment erosion in rivers, lakes, and the ocean, to pollutant r...