2,547 research outputs found
Periodic and solitary wave solutions of generalized nonlinear Schrödinger equation using a Madelung fluid description
No full textThe hydrodynamic fluid description, proposed many years ago by E. Madelung (1927) for quantum mechanics, is used to discuss the class of nonlinear Schr̈odinger equations. In the case of stationary profile solutions the equation satisfied by the fluid density ρ = {pipe}Ψ{pipe}2 is integrated and periodic solutions expressed through Jacobi elliptic functions are derived for cubic and cubic + quintic nonlinearities. In the limit case k2 = 1 the solitary wave solution found for the cubic + quintic nonlinearity proves to be much steeper and narrower than the one-soliton solution of the cubic NLS equation
Solitary waves in a Madelung Fluid Description of Derivative NLS equations
No full textRecently using a Madelung fluid description a connection between envelope-like solutions of
NLS-type equations and soliton-like solutions of KdV-type equations was found and investigated
by R. Fedele et al. (2002). A similar discussion is given for the class of derivative
NLS-type equations. For a motion with stationary profile current velocity the fluid density
satisfies generalized stationary Gardner equation, and solitary wave solutions are found. For
the completely integrable cases these are compared with existing solutions in literature
Modulational Instability of Cylindrical and Spherical NLS Equations. Statistical Approach
No full textThe modulational instability (Benjamin-Feir instability) for cylindrical and spherical NLS equations (c/sNLS equations) is studied using a statistical approach (SAMI). A kinetic equation for a two-point correlation function is written and analyzed using
Periodic and Solitary Wave Solutions of Two Component Zakharov-Yajima-Oikawa System, Using Madelung's Approach
No full textUsing the multiple scales method, the interaction between two bright and one dark solitons is studied. Provided that a long wave-short wave resonance condition is satisfied, the two-component Zakharov-Yajima-Oikawa (ZYO) completely integrable system is obtained. By using a Madelung fluid description, the one-soliton solutions of the corresponding ZYO system are determined. Furthermore, a discussion on the interaction between one bright and two dark solitons is presented. In particular, this problem is reduced to solve a one-component ZYO system in the resonance conditions
Periodic and stationary wave solutions of coupled NLS equations
No full textA system of coupled NLS equations (integrable and non-integrable) is discussed using a Madelung fluid description. The problem is equivalent with a two component fluid of densities ρ1 and ρ2 and velocities υ1 and υ2, which satisfy equations of continuity and equations of motion. Provided that the nonlinear coupling coefficients are identical, several periodic solutions, expressed through Jacobi elliptic functions, and localized solutions in the form of bright, dark and grey solitons were obtained in different simplifying conditions (motion with constant but equal velocities, i.e. υ1 = υ2 = υ, and equal "energies", i.e. E1 = E2 = E; motion with stationary profile of the current velocity). For different"energies" (E1 ≠ E2) a direct method is used, which can be easily extended to more complex situations (different nonlinear coupling coefficients, i.e. β and γ)
Madelung fluid description of generalized derivative NLS equation: special solutions and their stability
No full textA correspondence between the families of generalized nonlinear Schr¨odinger (NLS) equations and generalized KdV equations was recently found using a Madelung fluid description. We similarly consider a special derivative NLS equation. We find a number of solitary waves and periodic solutions (expressed in terms of elliptic Jacobi functions) for a motion with a stationary profile current velocity. We study the stability of a bright solitary wave (ground state) by conjecturing that the Vakhitov–Kolokolov criterion is
applicable
Assessing sustainability: Research directions and relevant issues
No full textThe growing research debate concerning sustainability and its applications in interdisciplinary domain represents a conjunction point where basic and applied science (scientific computation and applications in all areas of sciences, engineering, technology, industry, economics, life sciences and social sciences), but also qualified practitioners, compare and discuss advances in order to substance what we consider a the future perspective: “applied sustainability”. A relevant issue in order to compare and benchmark different position is the “sustainability performance assessment”. It means to discuss in a general view critical aspects and general issues in order to propose research directions and common parameters (indicators) to exchange and disseminate results and milestones in “sustainability” applications
On the mapping connecting the cylindrical nonlinear von Neumann equation with the standard von Neumann equation
No full textThe Wigner transformation is used to define the quasidistribution
(Wigner function) associated with the wave function of the cylindrical nonlinear Schroedinger equation (CNLSE) in a way similar to that of the standard nonlinear Schroedinger equation (NLS
Special Solutions of Some Generalized NLS Equations
No full textUsing a Madelung fluid description a discussion is given for some generalized NLS equations. Solitary wave and periodic solutions are obtained for constant and stationary profile current velocity
- …
