Singularity Theory is used to comprehensively investigate the bifurcations of the steady-states of the traveling wave ODEs of the cubic-quintic Ginzburg-Landau equation (CGLE). These correspond to plane waves of the PDE. In addition to the most general situation, we also derive the degeneracy conditions on the eight coefficients of the CGLE under which the equation for the steady states assumes...

A new analytical equation for prediction of temperature profile of a buried gas pipeline is developed. Utility of this equation is illustrated by its application to corresponding states principle. The resulting equation is tested through prediction of the actual Schorre data. It is shown that the new equation can predict temperature profile more accurately than the others without using any char...

Striped Turing patterns and solitary band and disk structures are constructed using a three-variable multiscale model with cubic nonlinearity and global control. The existence and stability conditions of regular structures are analysed using the equation of motion of curved boundaries between alternative states of the short-range component. The combined picture of transitions between striped an...

Medium Field Equation (MFE) multivariate public key cryptosystems were broken by High Order Linearization Equation (HOLE) attack. In order to avoid HOLE attack, we proposed an improvement of MFE, Cubic MFE public key encryption scheme. In our construction, multiplications of three second order matrices were used to get a set of cubic polynomials in the central map. Through theoretical analysis ...

For some of the EOS models the dimension of equilibrium problem can be reduced. Stability and difficulties in implementation are among the problems of flash calculation. In this work, a new reduction technique is presented to prepare a reduced number of equilibrium equations. Afterwards, a number of appropriate solution variables are selected for the prepared equation system to solve the equati...

Classes of solutions, asymptotic in small parameter , → 0, are constructed to the generalized nonlinear Schrödinger equation (NSE) in a multi-dimensional space with an external field in the framework of the WKB-Maslov method. Asymptotic semiclassically concentrated solutions (SCS), regarded as multi-dimensional solitary waves, are introduced for the NSE with an external field and cubic local no...