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

Contraction of variational principle and optical soliton solutions for two models of nonlinear Schrödinger equation with polynomial law nonlinearity

Our study analyzes the two models of the nonlinear Schrödinger equation (NLSE) with polynomial law nonlinearity by powerful and comprehensible techniques, such as the variational principle method and the amplitude ansatz method. We will derive the functional integral and the Lagrangian of these equations, which illustrate the system's dynamic. The solutions of these models will be extracted by selecting the trial ansatz functions based on the Jost linear functions, which are continuous at all intervals. We start with the Jost function that has been approximated by a piecewise linear function with a single nontrivial variational parameter in three cases from a region of a rectangular box, then use this trial function to obtain the functional integral and the Lagrangian of the system without any loss. After that, we approximate this trial function by piecewise linear ansatz function in two cases of the two-box potential, then approximate it by quadratic polynomials with two free parameters rather than a piecewise linear ansatz function, and finally, will be approximated by the tanh function. Also, we utilize the amplitude ansatz method to extract the new solitary wave solutions of the proposed equations that contain bright soliton, dark soliton, bright-dark solitary wave solutions, rational dark-bright solutions, and periodic solitary wave solutions. Furthermore, conditions for the stability of the solutions will be submitted. These answers are crucial in applied science and engineering and will be introduced through various graphs such as 2D, 3D, and contour plots

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

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

Mathematical methods via the nonlinear two-dimensional water waves of Olver dynamical equation and its exact solitary wave solutions

The problem formulations of the nonlinear for the small-long amplitude two-dimensional water waves propagation with free surface are studied. The water wave problem leads to the nonlinear Olver dynamical equation. By applying the extended mapping method, We derive the solitary wave solutions of the nonlinear Olver dynamical equation. These solutions for the nonlinear Olver dynamical equation are obtained efficiency and precisely of the method can be demonstrated. The movement role of the waves by making the graphs of the exact solutions and the stability of these solutions are analyzed and discussed. All solutions are stable and exact. Keywords: Shallow water waves, Solitary waves solutions, Extended mapping method, Mathematical physics method