A third-order nonlinear Schrodinger equation: The exact solutions, group-invariant solutions and conservation laws

In this study, we consider the third order nonlinear Schrodinger equation (TONSE) that models the wave pulse transmission in a time period less than one-trillionth of a second. With the help of the extended modified method, we obtain numerous exact travelling wave solutions containing sets of generalized hyperbolic, trigonometric and rational solutions that are more general than classical ones. Secondly, we construct the transformation groups which left the equations invariant and vector fields with the Lie symmetry groups approach. With the help of these vector fields, we obtain the symmetry reductions and exact solutions of the equation. The obtained group-invariant solutions are Jacobi elliptic function and exponential type. We discuss the dynamic behaviour and structure of the exact solutions for distinct solutions of arbitrary constants. Lastly, we obtain conservation laws of the considered equation by construing the complex equation as a system of two real partial differential equations (PDEs)

Multiple lump solutions and their interactions for an integrable nonlinear dispersionless PDE in vector fields

In this article, lump solutions, lump with I-kink, lump with II- kink, periodic, multiwaves, rogue waves and several other interactions such as lump interaction with II-kink, interaction between lump, lump with I-kink and periodic, interaction between lump, lump with II-kink and periodic are derived for Pavlov equation by using appropriate transformations. Additionally, we also present 3-dimensional, 2-dimensional and contour graphs for our solutions

An advanced delay-dependent approach of impulsive genetic regulatory networks besides the distributed delays, parameter uncertainties and time-varying delays

In this typescript, we concerned the problem of delay-dependent approach of impulsive genetic regulatory networks besides the distributed delays, parameter uncertainties and time-varying delays. An advanced Lyapunov–Krasovskii functional are defined, which is in triple integral form. Combining the Lyapunov–Krasovskii functional with convex combination method and free-weighting matrix approach the stability conditions are derived with the help of linear matrix inequalities (LMIs). Some available software collections are used to solve the conditions. Lastly, two numerical examples and their simulations are conferred to indicate the feasibility of the theoretical concepts

Stability Analysis of Traveling Wave Solutions for Generalized Coupled Nonlinear KdV Equations

In the present paper, an extended algebraic method is used for constructing exact traveling wave solutions for generalized coupled nonlinear KdV equations. By implementing the extended direct algebraic method, new exact solutions of the generalized coupled KdV equations are obtained. The present results are describing the generation and evolution of such waves, their interactions, and their stability. Moreover, the method can be applied to a wide class of coupled nonlinear evolution equations. The present traveling wave solutions have applications in physics

On the multi-waves, interaction and Peregrine-like rational solutions of perturbed Radhakrishnan-Kundu-Lakshmanan equation

In this work, we consider the perturbed Radhakrishnan-Kundu-Lakshmanan equation (RKL) which is the higher order nonlinear Schrodinger equation with cubic nonlinear terms in Kerr law. This equation is used to model propagation of solitons through an optical fiber. The multi-waves, interactions and Peregrine-like rational solutions of this equation are investigated with the aid of logarithmic transformation and symbolic computation without using Hirota bilinear forms By selecting appropriate values of the parameter, three dimensional plots are drawn to obtained solitons. Moreover, physical meanings of the solutions obtained were also presented

Ion acoustic solitary wave solutions of three-dimensional nonlinear extended Zakharov–Kuznetsov dynamical equation in a magnetized two-ion-temperature dusty plasma

We consider the propagation of three-dimensional nonlinear magnetized two-ion-temperature dusty plasma. The problem formulation of this mathematical model leads to nonlinear extended Zakharov–Kuznetsov (EZK) dynamical equation in three-dimensional by applying the reductive perturbation theory. We found the families of dust and ion solitary wave solutions of the three-dimensional nonlinear EZK dynamical equation using the auxiliary equation mapping method and direct algebraic mapping method. Keywords: Magnetized dusty plasma, Ion acoustic solitary waves, Extended Zakharov–Kuznetsov equation, Mathematical method

Bright and dark solitary wave soliton solutions for the generalized higher order nonlinear Schrödinger equation and its stability

The higher order nonlinear Schrödinger (NLS) equation describes ultra-short pluse propagation in optical fibres. By using the amplitude ansatz method, we derive the exact bright, dark and bright-dark solitary wave soliton solutions of the generalized higher order nonlinear NLS equation. These solutions for the generalized higher order nonlinear NLS equation are obtained precisely and efficiency of the method can be demonstrated. The stability of these solutions and the movement role of the waves are analyzed by applying the modulation instability analysis and stability analysis solutions. All solutions are exact and stable. MSC: 35G20, 35Q53, 37K10, 49S05, 76A60, Keywords: Generalized higher order NLS equation, Solitary wave solutions, Mathematical Physics method

New soliton solution to the longitudinal wave equation in a magneto-electro-elastic circular rod

This paper examines the effectiveness of an integration scheme which called the extended trial equation method (ETEM) in exactly solving a well-known nonlinear equation of partial differential equations (PDEs). In this respect, the longitudinal wave equation (LWE) that arises in mathematical physics with dispersion caused by the transverse Poisson’s effect in a magneto-electro-elastic (MEE) circular rod, which a series of exact traveling wave solutions for the aforementioned equation is formally extracted. Explicit new exact solutions are derived in different form such as dark solitons, bright solitons, solitary wave, periodic solitary wave, rational function, and elliptic function solutions of the longitudinal wave equation. The movements of obtained solutions are shown graphically, which helps to understand the physical phenomena of this longitudinal wave equation. Many other such types of nonlinear equations arising in non-destructive evaluation of structures made of the advanced MEE material can also be solved by this method. Keywords: Extended trial equation method, Longitudinal wave equation in a MEE circular rod, Dark solitons, Bright solitons, Solitary wave, Periodic solitary wav

Mathematical methods and solitary wave solutions of three-dimensional Zakharov-Kuznetsov-Burgers equation in dusty plasma and its applications

In this research article, a new technique for solving nonlinear complex physical phenomena, arising in different fields of science, is investigated, called Modified extended mapping method. The method is applied to three dimensional Zakharov-Kuznetsov-Burgers (ZKB) equation for the dust-ionacoustic waves in dusty plasmas. As a result, the exact and solitary wave solutions (which represent electric field potential), electric and magnetic fields and quantum statistical pressure for ZKB equation are obtained with the aid of Mathematica. These new exact solitary wave solutions are expressed in the forms of hyperbolic, trigonometric and rational functions. The graphical representations of the electric field potential and electric and magnetic fields are shown. These results demonstrate the efficiency and precision of the method that can be applied to many other mathematical physical problems. Keywords: Modified extended mapping method, 3-D Zakharov-Kuznetsov-Burgers equation, Exact and solitary wave solutions, Electric field potential, Electric and magnetic fields, Quantum statistical pressure, Graphical representatio