Search

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]

The optical solitons are extracted with Chen–Lee–Liu (CLL) equation that is considered with group velocity dispersion. The CLL equation describes the propagation of optical pulses in monomode fibers. In this article, the variety of solitons like dark, singular, dark-singular, bright-dark and periodic solutions are obtained by the mean of Fan-extended sub equation method under different constraint conditions. Moreover, for showing the physical interpretation of some recovered solutions, we also plot 3D maps by using the suitable values of involved parameters in solutions. The performance of the used method shows the adequate, validity and ability for implementation to many other nonlinear models. [ABSTRACT FROM AUTHOR]

Lump and their interactions with kink, periodic and rogue waves, and periodic cross lump waves will be studied for fifth-order variable coefficient nonlinear-Schrödinger equation in this paper. With the combinations of bilinear, exponent, and trigonometric functions, we'll study different lump soliton solutions. With interaction phenomenon we'll set up some new analytical solutions and also represents them in graphical ways. [ABSTRACT FROM AUTHOR]

In this paper, we will study Lengyel–Epstein (LE) system of chlorite iodide malonic acid (CIMA) chemical equations for bell-shaped, kink-type, and singular solutions. To get these solutions, we will use various integration schemes like sine–cosine approach (SCA), csch technique and tan - cot architectonic, respectively. We will also find some power series solutions for our governing model using residual power series method (RPSM) and provide a detailed comparison of exact and power series solutions. We also demonstrate our solutions graphically. [ABSTRACT FROM AUTHOR]

In this article, we construct multi-wave, homoclinic breather, M-shaped rational and periodic cross kink wave solutions for coupled-Higgs equation (CHE) by using distinct transformations. We obtain these solutions with the aid of logarithmic transformations and symbolic computations. Moreover, we also derive some soliton wave solutions for CHE in polynomial forms. These solutions include solitary wave, soliton wave and Jacobi elliptic function solutions and are found by implementing unified technique. We will also discuss the graphical structure of our newly achieved results. [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 article, we are interested to discuss the exact optical soiltons and other solutions in birefringent fibers modeled by Radhakrishnan–Kundu–Lakshmanan equation in two component form for vector solitons. We extract the solutions in the form of hyperbolic, trigonometric and exponential functions including solitary wave solutions like multiple-optical soliton, mixed complex soliton solutions. The strategy that is used to explain the dynamics of soliton is known as generalized exponential rational function method. Moreover, singular periodic wave solutions are recovered and the constraint conditions for the existence of soliton solutions are also reported. Besides, the physical action of the solution attained are recorded in terms of 3D, 2D and contour plots for distinct parameters. The achieved outcomes show that the applied computational strategy is direct, efficient, concise and can be implemented in more complex phenomena with the assistant of symbolic computations. The primary benefit of this technique is to develop a significant relationships between NLPDEs and others simple NLODEs and we have succeeded in a single move to get and organize various types of new solutions. The obtained outcomes show that the applied method is concise, direct, elementary and can be imposed in more complex phenomena with the assistant of symbolic computations [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]