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In this study, an effort has been made to obtain optical soliton solutions of the (1+1)-dimensional Biswas-Milovic equation which was introduced by Biswas and Milovic in 2010, having Kerr law and parabolic-law with weak non-local nonlinearity in the presence of spatio-temporal dispersion, which is one of the important models for nonlinear optics. Although, the model is an equation that has been studied by many researchers, the fact that the form to be examined has not been studied before. As a general algorithm, first converting the model to nonlinear ordinary differential form with a complex wave transformation, then obtaining candidate optical soliton solutions by utilizing the new Kudryashov technique, determining the ones that satisfy the main equation from these solutions as the exact solution, and in order to better understand the obtained solutions by making graphical presentation and providing the necessary comments constitute the main framework of the article. [ABSTRACT FROM AUTHOR]

In this study, an attempt to obtain optical soliton solutions of stochastic perturbed (1+1)-dimensional nonlinear Schrödinger equation having the Kerr law nonlinearity is presented. With the help of complex wave transform, the investigated nonlinear partial differential equation was converted into the nonlinear ordinary differential form. Analytical stochastic optical soliton solutions of the ordinary differential form were derived by applying the Kudryashov auxiliary equation method. By replacing the wave transformation and the appropriate solution set parameters, the main equation is provided. Graphic presentations were made for better interpretation of the results. [ABSTRACT FROM AUTHOR]

In the present study, we focus on obtaining the optical soliton solutions of the Drinfeld-Sokolov-Satsuma-Hirota (DSSH) equation using Kudryhashov methods. First, a wave transformation is applied to the DSSH equation, resulting in a nonlinear ordinary differential equation (NLODE). A balance number is deduced through the balancing of this NLODE. Subsequently, candidate solutions, inclusive of their respective derivatives and the wave transformation, are inserted into the DSSH equation. This results in an equation in polynomial form. Terms with equal power are grouped together in the new equation, and their coefficients are set to zero, leading to a system of algebraic equations. Solving this algebraic system facilitates the identification of undetermined parameters within the candidate solutions, thus yielding the solutions for the DSSH equation. Visualization of these solutions is executed through contour plots as well as two- and three-dimensional graphical representations. The contributions of this study are of substantial relevance for subsequent research in nonlinear science. [ABSTRACT FROM AUTHOR]

In this paper, we consider an effective technique based on wavelet collation method for solving time fractional Chafee-Infante equation. We transform the fractional differential equation to an algebraic equations system by using wavelet operational matrices of fractional integrals. We give an illustrative example to show the applicability and effectiveness of the method. We compare the exact and wavelet solutions in a table and figure. The results show that the method easily applicable to fractional differential equations [ABSTRACT FROM AUTHOR]

In this study, we have applied a generalized successive numerical technique to solve the elasticity problem of based on the elastic ground with variable coefficient. In the first stage, we have calculated the generalized successive approximation of being given BVP and in the second stage we have transformed it into Padé series. At the end of study a test problem has been given to clarify the method. [ABSTRACT FROM AUTHOR]

In this paper, a new collocation method based on Euler polynomials is improved for the numerical solution of generalized pantograph equations. This method transforms the generalized pantograph equations into the matrix equation with the help of Euler polynomials and collocation points. This matrix equation corresponds to a system of linear algebraic equations with the unknown Euler coefficients. By solving this system, the unknown Euler coefficients of the solution are found. Some numerical examples are given and comparisons with other methods are made in order to demonstrate the applicability and validity of the proposed method. [ABSTRACT FROM AUTHOR]

In this letter, numerical solutions of Cauchy problems are considered by multivariate Padé approximations (MPA). Multivariate Padé approximations (MPA) were applied to power series solutions of Cauchy problems that solved by using He’s variational iteration method (VIM). Then, numerical results obtained by using multivariate Padé approximations were compared with the exact solutions of Cauchy problems. [ABSTRACT FROM AUTHOR]