Search

In this article, the extended fan method and the positive quadratic function technique are used to solve the (2 + 1) -dimensional Chiral nonlinear Schrödinger equation. Several new outcomes are obtained. Several new results are obtained. We can offer soliton-type solutions, triangular-type solutions, simple and combined solutions using Jacobi's elliptic functions. Using suitable parameters, some graphics are given to observe the evolution of these analytical solutions. Many other nonlinear differential equations can benefit from using the methods proposed in this work. [ABSTRACT FROM AUTHOR]

The present study examines the nonlinear time-fractional model in the sense of a solitonic structure. A non-linear Schrödinger equation has applications in light scattering, indirect optical pulses as well as planer waves and to Bose-Einstein condensates enclosed in an anisotropic-shaped cigar, in a mean-field state, etc. A new extended direct algebraic method is utilized to get the soliton solutions with modified M-truncated and Atangana–Baleanu fractional operators which have Mittag-Leffler kernel. The obtained solutions contain new families of functions such as trigonometric, hyperbolic, rational, and exponential functions. The graphical 2D, 3D, contour, and also 3D spherical presentation pictorial the analysis with the feasible parametric values. On the evidence of the acquired solutions, it can be presumed that this technique is more effective and generalized to obtain solutions of many other non-linear partial differential equations that appear in different scientific disciplines. [ABSTRACT FROM AUTHOR]

This article deals with new soliton solutions of the generalized nonlinear Schrodinger equation with variable coefficients by the direct algebraic method. Once the variables of this technique are considered as special values. we could achieve the solitary waves that are unique from those attained by the other methods. It can be inferred that the solution methodology in conjunction with symbolic computing eligible to solve nonlinear partial differential equations precisely. [ABSTRACT FROM AUTHOR]

In this paper, we implemented extended e x p - φ ξ -expansion method for some exact solutions of (3 + 1)-dimensional nonlinear Schrödinger equation (NLSE) and coupled nonlinear Schrodinger's equation. The solutions we obtained are hyperbolic, trigonometric and exponential solutions. We observed that these solutions provided the equations through Mathematica 11.2. Apart from that, we have shown the graphics performance of some of the solutions found. This method has been used recently to obtain exact traveling wave solutions of nonlinear partial differential equations. The results achieved in this study have been confirmed with computational software Maple or Mathematica by placing them back into NLFPDEs and found them correct. We posited that the approach is updated to be more pragmatic, efficacious, and credible and that we pursue more generalized precise solutions for traveling waves, like the solitary wave solutions. [ABSTRACT FROM AUTHOR]

In this paper and for the first time, we describe and introduce a new extended direct algebraic method which is a new method for solving nonlinear partial differential equations arising in nonlinear optics and nonlinear science. By applying this method, we have constructed new solitary wave solutions for the unstable Schrödinger equation. A large family of traveling wave type exact solutions covering exponential, generalized trigonometric, rational and generalized hyperbolic functions to this equation is determined. The solutions are expressed in explicit forms. [ABSTRACT FROM AUTHOR]

Solving partial differential equations has always been one of the significant mathematical tools for modeling applied phenomena in various fields. In this paper, our main motivation is to find the traveling wave solutions of unstable nonlinear Schrödinger equation (UNLSE) which describes the two layer baroclinic instability, and two lossless symmetric stream plasma instability, and also disturbance of time period in both stable and unstable media. The methods which are used to endure these solutions are extended rational sine-cosine/sinh-cosh. New solutions are constructed in the different forms such as hyperbolic and trigonometric. The achieved results present that proposed techniques are consequential for exploring several types of nonlinear partial differential equations (NLPDEs) in applied sciences and solutions are presented in the form of novel periodic, dark, bright, and periodically bright solitons. These methods are highly effective, robust, and provide an alternative approach for establishing new soliton solutions for various types of partial differential equations (PDEs) used in mathematical physics. [ABSTRACT FROM AUTHOR]

Presented herein is an exact examination on the resonant nonlinear Schrödinger equation (RNLSE) with Kerr law nonlinearity considering inter-modal dispersion and spatio-temporal. To this end, the ordinary differential equation (ODE) is derived from the traveling wave transformation. Then, the new extended direct algebraic method (NEDAM) is utilized in the axial direction to obtain the results of this study. Subsequently, a bunch of optical soliton solutions in conjunction with dark, bright, and dark-bright soliton solutions are plotted. As a result, it is verified the methodology has an effective mathematical gadget to solve nonlinear partial differential equations (NPDEs). [ABSTRACT FROM AUTHOR]