in this paper, we obtained the 1-soliton solutions of the symmetric regularized long wave (srlw) equation and the (3+1)-dimensional shallow water wave equations. solitary wave ansatz method is used to carry out the integration of the equations and obtain topological soliton solutions the physical parameters in the soliton solutions are obtained as functions of the dependent coefficients. note t...

In this manuscript, we investigate solutions of the partial differential equations (PDEs) arising inmathematical physics with local fractional derivative operators (LFDOs). To get approximate solutionsof these equations, we utilize the reduce differential transform method (RDTM) which is basedupon the LFDOs. Illustrative examples are given to show the accuracy and reliable results. Theobtained ...

Combining recent moment and sparse semidefinite programming (SDP) relaxation techniques, we propose an approach to find smooth approximations for solutions of nonlinear differential equations. Given a system of nonlinear differential equations, we apply a technique based on finite differences and sparse SDP relaxations for polynomial optimization problems (POP) to obtain a discrete approximatio...

The dynamic analysis of the biomechanical model of the head load impact using the Differential Transform Method is presented in this paper. In many parts of the world, the problem of traumatic brain injuries (TBI) has led to neurodegenerative dementing disorders and diseases as a result of head load impact from sporting activities, accidents involving the head, etc. have serious effects on huma...

In this paper we introduce some stability criteria for impulsive fuzzy system of differential equations with finite delay in states. Firstly, a new comparison principle for fuzzy differential system compared to crisp ordinary differential equation, based on a notion of upper quasi-monotone nondecreasing, in N dimentional state space is presented. Furthermore, in order to analyze the stability o...

in this paper, non-polynomial spline method for solving coupled burgers’ equations are presented. we take a new spline function. the stability analysis using von-neumann technique shows the scheme is unconditionally stable. to test accuracy the error norms2l, ∞l are computed and give two examples to illustrate the sufficiency of the method for solving such nonlinear partial differential equatio...

Taking the example of Koretweg–de Vries equation, it is shown that soliton solutions need not always be the consequence of the trade-off between the nonlinear terms and the dispersive term in the nonlinear differential equation. Even the ordinary one dimensional linear partial differential equation can produce a soliton. Solitary waves and solitons are often described [1-8] as a consequence of ...

In this article the nonlinear mixed Volterra-Fredholm integral equations are investigated by means of the modied three-dimensional block-pulse functions (M3D-BFs). This method converts the nonlinear mixed Volterra-Fredholm integral equations into a nonlinear system of algebraic equations. The illustrative   examples are provided to demonstrate the applicability and simplicity of our   scheme.