Soliton theory and modulation instability analysis: The Ivancevic option pricing model in economy

In this projected paper, we study on the Ivancevic option pricing model. We apply two important methods, namely, rational sine-Gordon expansion method which is recently developed, and secondly, modified exponential method. Via these methods, we obtain some important properties of Ivancevic option pricing model. We extract many solutions such as complex, periodic, dark bright, mixed dark-bright, singular, travelling and hyperbolic functions. We investigate the option price wave functions of dependent variable, and also, observe the modulation instability analysis in detail. Furthermore, we report the strain conditions for the valid solutions under the family conditions, as well. We simulate the 2D, 3D and counter plots by choosing the suitable values of the parameters involved. Finally, we present the top and low points of pricing in the mentioned intervals via contour simulations. (C) 2022 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University

The Modified Trial Equation Method for Fractional Wave Equation and Time Fractional Generalized Burgers Equation

The fractional partial differential equations stand for natural phenomena all over the world from science to engineering. When it comes to obtaining the solutions of these equations, there are many various techniques in the literature. Some of these give to us approximate solutions; others give to us analytical solutions. In this paper, we applied the modified trial equation method (MTEM) to the one-dimensional nonlinear fractional wave equation (FWE) and time fractional generalized Burgers equation. Then, we submitted 3D graphics for different value of

On the modulation instability analysis and deeper properties of the cubic nonlinear Schr¨odinger’s equation with repulsive δ-potential

This projected work applies the generalized exponential rational function method to extract the complex, trigonometric, hyperbolic, dark bright soliton solutions of the cubic nonlinear Schrödinger’s equation. Moreover, trigonometric, complex, strain conditions and dark-bright soliton wave distributions are also reported. Furthermore, the modulation instability analysis is also studied in detail. To better understand the dynamic behavior of some of the obtained solutions, several numerical simulations are presented in the paper. According to the obtained results, it is clear that the method has less limitations than other methods in determining the exact solutions of the equations. Despite the simplicity and ease of use of this method, it has a very powerful performance and is able to introduce a wide range of different types of solutions to such equations. The idea used in this paper is readily applicable to solving other partial differential equations in mathematical physics.Fundación Séneca (Spain), grant 20783/PI/18., and Ministry of Science, Innovation and Universities (Spain), grant PGC2018-097198-B- 100. Moreoer, this projected work was partially (not financial) supported by Harran University with the project HUBAP ID:20124

New classifications of nonlinear Schrödinger model with group velocity dispersion via new extended method

This work investigates the nonlinear Schrödinger equation (NLSE) with group velocity dispersion and second order spatiotemporal dispersion coefficients. The governing model is reduced into the classical nonlinear ordinary differential equation. Extended direct algebraic method (EDAM) is implemented to construct many novel mixed dark, and complex optical solutions. As a result, some important analytical solutions such as travelling mixed dark, and complex travelling wave solutions for the model are extracted.</p

Complex Soliton Solutions to the Gilson–Pickering Model

In this paper, an analytical method based on the Bernoulli differential equation for extracting new complex soliton solutions to the Gilson&#8315;Pickering model is applied. A set of new complex soliton solutions to the Gilson&#8315;Pickering model are successfully constructed. In addition, 2D and 3D graphs and contour simulations to the complex soliton solutions are plotted with the help of computational programs. Finally, at the end of the manuscript a conclusion about new complex soliton solutions is given

Regarding new wave distributions of the non-linear integro-partial Ito differential and fifth-order integrable equations

This paper applies a powerful scheme, namely Bernoulli sub-equation function method, to some partial differential equations with high non-linearity. Many new travelling wave solutions, such as mixed dark-bright soliton, exponential and complex domain, are reported. Under a suitable choice of the values of parameters, wave behaviours of the results obtained in the paper – in terms of 2D, 3D and contour surfaces – are observed

Extraction Complex Properties of the Nonlinear Modified Alpha Equation

This paper applies one of the special cases of auxiliary method, which is named as the Bernoulli sub-equation function method, to the nonlinear modified alpha equation. The characteristic properties of these solutions, such as complex and soliton solutions, are extracted. Moreover, the strain conditions of solutions are also reported in detail. Observing the figures plotted by considering various values of parameters of these solutions confirms the effectiveness of the approximation method used for the governing model

Regarding new wave distributions of the non-linear integro-partial Ito differential and fifth-order integrable equations

This paper applies a powerful scheme, namely Bernoulli sub-equation function method, to some partial differential equations with high non-linearity. Many new travelling wave solutions, such as mixed dark-bright soliton, exponential and complex domain, are reported. Under a suitable choice of the values of parameters, wave behaviours of the results obtained in the paper – in terms of 2D, 3D and contour surfaces – are observed

An Effective Schema for Solving Some Nonlinear Partial Differential Equation Arising In Nonlinear Physics

In this paper, a new computational algorithm called the "Improved Bernoulli sub-equation function method" has been proposed. This algorithm is based on the Bernoulli Sub-ODE method. Firstly, the nonlinear evaluation equations used for representing various physical phenomena are converted into ordinary differential equations by using various wave transformations. In this way, nonlinearity is preserved and represent nonlinear physical problems. The nonlinearity of physical problems together with the derivations is seen as the secret key to solve the general structure of problems