• Soliton Solution of Nonlinear Schodniger Equation Using Hirota Method 

  Zelalem, Getahun (Ambo University, 2025-03)

  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 ...
• ” Some Properties Of Fractional Bernoulli Polynomials” 

  Geleta, Waktasu (Ambo University, 2024-09)

  In this thesis we establish some properties of fractional Bernoulli numbers and fractional Bernoulli polynomials which are analogous to fractional exponential function. We also investigate the fraction Bernoulli numbers ...
• ” Carlitz type and Bernoulli Identities” 

  Dereje, Boka (Ambo University, 2024-05)

  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 ...
• Traveling Wave Solution Method For The Generalized Kuramoto-Sivashinsky Equation 

  Yadesa, Hirpa (Ambo University, 2024-11)

  The generalized Kuramoto-Sivashinsky (GKS) equation is an important nonlinear partial differential equation (PDE) that models various physical phenomena, including plasma instabilities, reaction-diffusion systems, and ...
• Comparison Between The Homotopy Analysis Method And Homotopy Perturbation Method To Solve Two Dimensional Nonlinear Schr Odinger Equations With External Potentials 

  Alemayehu, Dejash (Ambo University, 2024-07)

  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 ...
• “Soliton Solutions of the Generalized Third-Order Nonlinear Schr¨Odinger Equation In (1 + 1) Dimension By Hyperbolic Function Method” 

  Daniel, Derara (Ambo University, 2024-10)

  In this thesis, the main purpose is to find the soliton solution of third order nonlinear Schro¨dinger equations in (1 + 1)− dimension. The hyperbolic function method is applied to find a solution of (1 + 1)−dimensional ...
• A New Class of Generalized Polynomials Associated with Hermite and Bernoulli Polynomials 

  Bedatu, Worki (Ambo University, 2024-04)

  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 ...
• ”Application Of The First Integral Method To Solve Traveling Wave Of Non-Linear Physical Models” 

  Duguma, Legese (Ambo University, 2024-08)

  In this thesis, the First Integral method is applied to construct an exact Travelling Wave solu tion of (2 + 1)−dimensional nonlinear Boussenesq equation. It is shown that the method pro vides a powerful mathematical tool ...
• Traveling Wave Solutions To The Nonlinear Evolution Equation In (2+1)-Dimensional Using Tanh Method 

  Asnake, Getachew (Ambo University, 2024-07)

  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, ...
• Homotopy Analysis And Homotopy Perturbation Method For Solving Fractional Acousticswave Equation 

  Turi, Refera (Ambo University, 2024-07)

  This study focused on solving fractional acoustic wave equations, which are essential for understanding systems characterized by long-range interactions or anomalous diffusion. Fractional differential equations (FDEs), ...
• Bright And Dark Solitary Wave Soliton Solutions For The Generalized Higher Order Nonlinear Schro¨ Dinger Equation And Its Stability 

  Merga, Takele (Ambo University, 2024-07)

  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 ...
• Formation And Propagation Of Singularities In One Dimensional Nonlinear Wave Equation By Variational Method 

  Tulu, Negash (Ambo University, 2024-07)

  The propagation of singularities for nonlinear wave equations, that is, the relation between the singularities of the initial data and the singularities of the solution is well understood. In this studyWe prove that ...
• Mesh less Method for Solution Of Delay Parabolic Partial Differential Equations 

  Dereje, Gurmesa (Ambo University, 2024-07)

  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 ...
• Radial Basis Function Method For Solution Of Two-Dimensional Wave Equation 

  Berhanu, Bedada (Ambo University, 2024-07)

  This study presents a numerical scheme radial basis function (RBF) method for solving the two dimensional wave equation. The RBF method, known for its flexibility and accuracy in handling complex geometries, is applied ...
• On The Generalized Euler Polynomials Of The Second Kind 

  Daba, Negassa (Ambo University, 2024-06)

  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 ...
• Existence Of Solitary Wave Solutions Of Singularly Perturbed Korteweg-De Vries Equation By Tanh Method 

  Bira, Bejiga (Ambo University, 2024-08)

  In this thesis, the existence of solitory wave solutions of singularly perturbed Korteweg de Vries equation is investigated by tanh method and the solution has been successfully obtained by this method. Finally, it is ...
• Degenerate Cauchy Numbers and Polynomials of the Second Kind. 

  Petros, Ajema (Ambo University, 2024-05)

  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 ...
• The Laplace And Mellin Transforms Of Powers Of The Riemann Zeta Function 

  Dejene, Ararsa (Ambo University, 2024-04)

  This paper gives a survey of known results concerning the Laplace transform Lk(s) := Z ¥ 1 jz ( 1 2 +ix)j2ke􀀀sx dx (k 2 N, Âe(s) > 0 ) and the (modified) Mellin transform Zk(s) := Z ¥ 1 jz ( 1 2 +ix)j2kx􀀀s ...
• Solutions For Rosenau-Hyman Equations By Using Multiple Scale Perturbation Method 

  Girma, Atomsa (Ambo University, 2024-05)

  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 ...
• Explicit And Identities For Gamma Function And Hy Pergeometric Function 

  Tulu T, Tafa (Ambo University, 2024-04)

  Equations involving the gamma and hypergeometric functions are of great interest to mathematicians and scientists, and newly proven iden tities for these functions assist in nding solutions to di erential and integral ...

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