For the Coupled Nonlinear Schrödinger Equations (CNLSE) we construct a conservative fully implicit scheme (in the vein of the scheme with internal iterations proposed in [C.I. Christov, S. Dost, G.A. Maugin, Inelasticity of soliton collisions in system of coupled nls equations, Physica Scripta...

A fully implicit finite difference scheme is developed for the stream function formulation of unsteady thermoconvective flows. An artificial time is added in the equation for the stream function rendering it into an ultra-parabolic type. For each time stage of the real time, a convergence is...

The system of coupled nonlinear Schrödinger’s equations (CNLSE) is considered and the physical meaning of the coupling terms is identified. The attention is focused on the case of real-valued parameter of linear cross-diffusion. A new analytical solution for the coupled case is found and used...

We develop a Fourier–Galerkin spectral technique for computing the solutions of type of interacting localized waves. To this end, a special complete orthonormal system of functions in L2(−∞,∞) is used and a time-stepping algorithm implementing the spectral method is developed. The rate...

In recent works of the author [Found. Phys. 36 (2006) 1701–1717; Math. Comput. Simul. 74 (2007) 93–103], the argument has been made that Hertz's equations of electrodynamics reflect the material invariance (indifference) of the latter. Then the principle of material invariance was postulated in...

We develop a Fourier–Galerkin spectral technique for computing the stationary solutions of 2D generalized wave equations. To this end a special complete orthonormal system of functions in L2(−∞,∞) is used for which product formula is available. The exponential rate of convergence is...

We investigate numerically the collision dynamics of elliptically polarized solitons of the System of Coupled Nonlinear Schrödinger Equations (SCNLSE) for various different initial polarizations and phases. General initial elliptic polarizations (not sech-shape) include as particular cases the...

The Klein—Gordon equation with cubic nonlinearity (the φ4 equation) is considered and an energy-conserving difference scheme is proposed for its solution. The scheme, extended to finite time increments and spacing, is then used to define a coupled map lattice for which an energy-like...