The symmetry group method is applied to a generalized Korteweg-de Vries equation and several classes of group invariant solutions for it are obtained by means of this technique. Polynomial, trigonometric, and elliptic function solutions can be calculated. It is shown that this generalized equation can be reduced to a first-order equation under a particular second-order differential constraint w...

The systems approach is a means of studying the properties of things in relation, not just to their components, but also to the ways in which the components interact, both with each other and with their environment. Within this approach, the task of ascertaining causal linkages existing among the variables in soft systems (as against hard systems) is more complex as these are often messy and th...

An indefinite stochastic Riccati Equation is a matrix-valued, highly nonlinear backward stochastic differential equation together with an algebraic, matrix positive definiteness constraint. We introduce a new approach to solve a class of such equations (including the existence of solutions) driven by one-dimensional Brownian motion. The idea is to replace the original equation by a system of BS...

Energy equation for turbulent flow in a rotating system was derived in terms of second order correlation tensors, where the correlation tensors were functions of space coordinates, distance between two points and time. To reveal the relationship of turbulent energy between two points, one point was taken as origin of the coordinate system. Due to rotation, the Coriolis force played an important...

This paper introduces a relative structural complexity measure for the characterization of disordered surfaces. Numerical solutions of 2d+1 KPZ equation and scanning force microscopy (SFM) patterns of porous silicon samples are analyzed using this methodology. The results and phenomenological interpretation indicate that the proposed measure is efficient for quantitatively characterize the stru...

The Hartree-Fock-Bogoliubov equation for the ground states of even-even atomic nuclei is solved using the canonical representation in the coordinate space for zero range interactions like the Skyrme force. The gradient method is improved for faster convergence to the solutions under constraint of orthogonality between canonical orbitals. Necessity of the cut-off of the pairing interaction is sh...

Fractional dynamics of relativistic particle is discussed. Derivatives of fractional orders with respect to proper time describe long-term memory effects that correspond to intrinsic dissipative processes. Relativistic particle subjected to a non-potential four-force is considered as a nonholonomic system. The nonholonomic constraint in fourdimensional space-time represents the relativistic inv...

We outline a general methodology to infer the inductive velocity field vector in solar active regions. For the first time, both the field-aligned and the crossfield velocity components are reconstructed. The cross-field velocity solution accounts for the changes of the vertical magnetic field seen between a pair of successive active-region vector magnetograms via the ideal induction equation. T...