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In this paper, we will find the chirped solitons (CS) solutions to the nonlinear schrödinger's equation (NLSE) under polynomial nonlinearity with spatio temporal dispersion (STD) and group velocity dispersion (GVD). We will find CS with Jacobi elliptic functions (JEF). We will also get some new solitary waves (SW) like bright, dark, kink, periodic, hyperbolic, and other solutions. The dynamical behaviour for these waves will also be discussed along with constraint conditions. [ABSTRACT FROM AUTHOR]

The focus of this article is to find some new exact solutions to the (2+1)-dimensional nonlinear Schrödinger equation (NLSE) with Kerr media by employing the auxiliary equation method. A set of novel travelling wave solutions are observed such as bright, dark, periodic and optical solitons (dromions). Moreover, the physical interpretation of nonlinear waves would also be demonstrated with the aid of scientific computing. [ABSTRACT FROM AUTHOR]

In this paper, we investigate resonanat nonlinear Schrödinger equation (RNLSE) with self steeping phenomena to obtain some chirped periodic (CP) and soliton waves. A chirp is a signal in which the frequency increases (up chirp) or decreases (down-chirp) with time. It is commonly used in sonar, radar and laser systems and in other applications, such as in spread-spectrum communications. We obtain chirped periodic waves (CPW) with some Jacobi elliptic functions (JEF). We also obtain some solitary waves (SW) like dark, bright, singular waves of type I and II, hyperbolic, periodic and other solutions. The dynamical behaviour for these waves will also be presented. [ABSTRACT FROM AUTHOR]

This paper retrives hyperbolic, periodic, singular, domain walls, dark-like dromions (solitons) for perturbed fractional nonlinear Schrödinger equation. We use a quite new technique known as extended modified auxiliary equation mapping method. This method is quite effective and delivers so many new dromions. We used conformable derivatives for our perturbed fractional NLSE with some constraint conditions. [ABSTRACT FROM AUTHOR]

In this study, we extract the different kinds of exact wave solutions to the (1+1) dimensional Chiral nonlinear Schrödinger equation (CNLSE) that describes the edge states of the fractional quantum hall effect in quantum field theory. The extended rational sine–cosine/sinh–cosh techniques are utilized for obtaining solutions. Parametric conditions on physical parameters are also enumerated to ensure the existence criteria of soliton solutions. Moreover, the stability analysis is also discussed. By the suitable selection of parameters, three dimensional, two dimensional and contour plots are sketched. The obtained outcomes show that the applied computational strategies are direct, efficient, concise and can be implemented in more complex phenomena with the assistant of symbolic computations. [ABSTRACT FROM AUTHOR]

The focus of this article is to find some new exact solutions to the M-fractional paraxial nonlinear Schrödinger equation with Kerr media by employing the modified simple equation method and the auxiliary equation method. A set of novel travelling wave solutions are observed such as bright, dark, periodic and optical solitons. Moreover, the physical interpretation of nonlinear waves would also be demonstrated with the aid of scientific computing. [ABSTRACT FROM AUTHOR]