相关论文: Generalized and new solutions of the NRT nonlinear…
We present a new generalization of the well-known power-type Sundman transformation, involving not only powers of the function but also of its derivative, along with its inverse. Our aim is to explore the use of such transformations in the…
We report on the time dependent solutions of the $q-$generalized Schr\"odinger equation proposed by Nobre et al. [Phys. Rev. Lett. 106, 140601 (2011)]. Here we investigate the case of two free particles and also the case where two particles…
The nonlinear Schrodinger equation is well known as a universal equation in the study of wave motion. In the context of wave motion at the free surface of an incompressible fluid, the equation accurately predicts the evolution of modulated…
For the first time, a nonlinear Schr\"odinger equation of the general form is considered, depending on time and two spatial variables, the potential and dispersion of which are specified by two arbitrary functions. This equation naturally…
We obtain time dependent $q$-Gaussian wave-packet solutions to a non linear Schr\"odinger equation recently advanced by Nobre, Rego-Montero and Tsallis (NRT) [Phys. Rev. Lett. 106 (2011) 10601]. The NRT non-linear equation admits plane…
For the first time, the general nonlinear Schr\"odinger equation is investigated, in which the chromatic dispersion and potential are specified by two arbitrary functions. The equation in question is a natural generalization of a wide class…
By applying a simple symmetry reduction on a two-layer liquid model, a nonlocal counterpart of it is obtained. Then a general form of nonlocal nonlinear Schrodinger (NNLS) equation with shifted parity, charge-conjugate and delayed time…
We use a fractional transformation to connect the traveling wave solutions of the nonlinear Schr\"odinger equation (NLSE), phase-locked with a source, to the elliptic functions satisfying, $f^{\prime\prime}\pm af\pm \lambda f^{3}=0$. The…
Interesting nonlinear generalization of both Schr\"odinger's and Klein-Gordon's equations have been recently advanced by Tsallis, Rego-Monteiro, and Tsallis (NRT) in [Phys. Rev. Lett. {\bf 106}, 140601 (2011)]. There is much current…
The existence of nonzero periodic travelling wave solutions for a general discrete nonlinear Schr\"odinger equation (DNLS) on finite one-dimensional lattices is proved. The DNLS features a general nonlinear term and variable range of…
The damped isothermal Euler equations, the Smoluchowski equation and the damped logarithmic Schr\"odinger equation with a harmonic potential admit stationary and self-similar solutions with a Gaussian profile. They satisfy an $H$-theorem…
The nonlinear Schr\"odinger equation (NLSE) is a rich and versatile model, which in one spatial dimension has stationary solutions similar to those of the linear Schr\"odinger equation as well as more exotic solutions such as solitary waves…
In this paper, we present the two-dimensional generalized nonlinear Schr\"odinger equations with the Lax pair. These equations are related to many physical phenomena in the Bose-Einstein condensates, surface waves in deep water and…
It has been found a simple procedure for the general solution of the time-independent Schr\"odinger equation (SE) with the help of quantization of potential area in one dimension without making any approximation. Energy values are not…
With the stationary solution assumption, we establish the connection between the nonlocal nonlinear Schr\"{o}dinger (NNLS) equation and an elliptic equation. Then, we obtain the general stationary solutions and discuss the relevance of…
In this paper we study radial solutions of certain two-dimensional nonlinear Schr\"odinger equation with harmonic potential, which is supercritical with respect to the initial data. By combining the nonlinear smoothing effect of Schr…
A periodic two-phase algebro-geometric solution of the focusing nonlinear Schr\"odinger equation is constructed in terms of elliptic Jacobi theta-functions. A dependence of this solution on the parameters of a spectral curve is…
We obtain exact moving and stationary, spatially periodic and localized solutions of a generalized discrete nonlinear Schr\"odinger equation. More specifically, we find two different moving periodic wave solutions and a localized moving…
In this note, we generalize the nonlinearity-recovery result in [7] for classical cubic nonlinear Schr\"odinger equations to higher-order Schr\"odinger equations with a more general nonlinearity. More precisely, we consider a…
In this paper, traveling wave solutions to the nonlinearly dispersive Schr\"odinger equation are given in the case of one-dimensional non-relativistic electron confined to a cylindrical quantum well. Investigations gave evidence to the…