The nonlinear Schrdinger equation with the effects of third-order by using Bilinear Hirota method, the analytic solutions of this model are obtained. According to those solutions, the relevant properties and features of ...

By using an explicit formula for Bernoulli polynomials we ob tained in a recent work Bn(y)is written as a linear combination of the(y −r) n ; r = 1, 2, 3, · · · k + 1 where k ≥ n polynomials it is pos sible to obtain ...

Most of nonlinear partial di erential equations have many application in physical world. Moreover, the solutions of nonlinear partial di erential equations are not easily solvable and hence di erent methods were applied ...

In this thesis we consider a new class of generalized polynomials associated with Hermite and Bernoulli polynomials of degree n and order . The concepts of Bernoulli numbers, Bernoulli polynomials, generalized Bernoulli ...

This study focused on traveling wave solutions to the nonlinear evolution equation in (2+1)- dimensional using tanh method. The System of linear equations plays a major role in various areas of sciences such as mathematics, ...

The current study examines the stability of both bright and dark solitary wave solutions for the Generalized Higher Order Nonlinear Schr¨odinger Equation and its Stability. The propagation of ultrashort pulses in nonlinear ...

In this thesis, we present a numerical method for solving delay differential equations (DDEs). The method utilizes radial basis functions (RBFs). Error analysis is presented for this method. Finally, numerical examples ...

Many mathematicians have studied varies relations between Euler numbers En, Bernoulli numbers Bn and Genocchi numbers Gn. They have found numerous important applications in number theory. In this thesis we explain the ...

In this thesis, we consider some generalization of Degenerate Cauchy Numbers and Polynomials of the Second Kind. The generalization is by means of definite integral and generating functions. All these generalizations ...

Nonlinear partial differential equations are important in real physical world. However, finding the solutions of nonlinear Rosenau Hyman equations are full of complex. The main purpose of multiple scala perturbation ...