The Infona portal uses cookies, i.e. strings of text saved by a browser on the user's device. The portal can access those files and use them to remember the user's data, such as their chosen settings (screen view, interface language, etc.), or their login data. By using the Infona portal the user accepts automatic saving and using this information for portal operation purposes. More information on the subject can be found in the Privacy Policy and Terms of Service. By closing this window the user confirms that they have read the information on cookie usage, and they accept the privacy policy and the way cookies are used by the portal. You can change the cookie settings in your browser.
As an introduction to the special issue on nonlinear waves, solitons and their significance in physics are reviewed. The soliton is the first universal concept in nonlinear science. Universality and ubiquity of the soliton concept are emphasized.
A tutorial review is presented of the use of direct variational methods based on Rayleigh-Ritz optimization for finding approximate solutions to various nonlinear evolution equations. The practical application of the approach is demonstrated by some illustrative examples in connection with the nonlinear Schrödinger equation.
A class of nonlinear Schrödinger-type equations, including the Rangwala-Rao equation, the Gerdjikov-Ivanov equation, the Chen-Lee-Lin equation and the Ablowitz-Ramani-Segur equation are investigated, and the exact solutions are derived with the aid of the homogeneous balance principle, and a set of subsidiary higher order ordinary differential equations (sub-ODEs for short).
We review a recent asymptotic weak noise approach to the Kardar-Parisi-Zhang equation for the kinetic growth of an interface in higher dimensions. The weak noise approach provides a many-body picture of a growing interface in terms of a network of localized growth modes. Scaling in 1d is associated with a gapless domain wall mode. The method also provides an independent argument for the existence...
In this paper, we obtain exact soliton solutions of the modified KdV equation, inhomogeneous nonlinear Schrödinger equation and G(m, n) equation with variable-coefficients using solitary wave ansatz. The constraint conditions among the time-dependent coefficients turn out as necessary conditions for the solitons to exist. Numerical simulations for dark and bright soliton solutions for the mKdV equation...
We present new types of compacton-like solutions for modified KdV and nonlinear Schrödinger equation with external sources, using a recently developed fractional transformation. In particular, we explicate these novel compactons for the trigonometric case, and compare their properties with those of the compactons and solitons in the case of modified KdV equation. Keeping in mind the significance of...
The nonlinear wave modulation of planar and non-planar (cylindrical and spherical) dust-acoustic waves (DAW) propagating in dusty plasmas, in the presence of non-extensive distributions for ions and electrons is investigated. By employing multiple scales technique, a cylindrically and spherically modified nonlinear Schrödinger equation (NLSE) is derived. The presence of hot non-extensive ...
In this paper, a unified formula of a series of rogue wave solutions for the standard (1+1)-dimensional nonlinear Schrödinger equation is obtained through exp-function method. Further, by means of an appropriate transformation and previously obtained solutions, rogue wave solutions of the variable coefficient Schrödinger equation are also obtained. Two free functions of time t and several arbitrary...
Smooth and non-smooth optical solitons in the nonlinearly dispersive Schrödinger equation are given by phase portraits. The Melnikov technique is used to detect conditions for chaotic motion of this deterministic system and to analyse conditions for the suppression of chaos. Our results show that the system is in a state of Melnikov chaos by external disturbances. After the implementation of the controlled...
The nonlinear propagation of cylindrical and spherical dust-ion-acoustic (DIA) envelope solitary waves in unmagnetized dusty plasma consisting of dust particles with opposite polarity and non-extensive distribution of electron is investigated. By using the reductive perturbation method, the modified nonlinear Schrödinger (NLS) equation in cylindrical and spherical geometry is obtained. The modulational...
From a generic transformation, a (3 $$+$$ + 1)-dimensional nonlinear Schrödinger equation with spatially modulated nonlinearity is studied and exact spatiotemporal soliton cluster solutions are derived. When the azimuthal parameter $$m = 0$$ m = 0 , Gaussian solitons are constructed. For the modulation depth $$q = 1$$ q = 1 and the azimuthal parameter $$m\ne 0$$ ...
We describe analytically the nonlinear surface waves at the interface between two nonlinear media with different characteristics. We use one-dimensional nonlinear Schrödinger equation with cubic nonlinearity differing on the opposite sides of the interface. We take into account the interaction of excitations with media interface. We consider the interaction of the wave with the interface using the...
Set the date range to filter the displayed results. You can set a starting date, ending date or both. You can enter the dates manually or choose them from the calendar.