Fadi Awawdeh


2 New Exact Three-Wave Solutions for the (2+1)-Dimensional Asymmetric Nizhnik-Novikov-Veselov System

Authors: Fadi Awawdeh, O. Alsayyed


New exact three-wave solutions including periodic two-solitary solutions and doubly periodic solitary solutions for the (2+1)-dimensional asymmetric Nizhnik-Novikov- Veselov (ANNV) system are obtained using Hirota's bilinear form and generalized three-wave type of ansatz approach. It is shown that the generalized three-wave method, with the help of symbolic computation, provides an e¤ective and powerful mathematical tool for solving high dimensional nonlinear evolution equations in mathematical physics.

Keywords: Hirota bilinear method, soliton solution, ANNV System

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1183
1 On a Class of Inverse Problems for Degenerate Differential Equations

Authors: Fadi Awawdeh, H.M. Jaradat


In this paper, we establish existence and uniqueness of solutions for a class of inverse problems of degenerate differential equations. The main tool is the perturbation theory for linear operators.

Keywords: Inverse problem, Degenerate Differential Equations, Perturbation Theory for Linear Operators

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1363


3 Analysis of a Generalized Sharma-Tasso-Olver Equation with Variable Coefficients

Authors: Fadi Awawdeh, O. Alsayyed, S. Al-SharĂ¡


Considering the inhomogeneities of media, the variable-coefficient Sharma-Tasso-Olver (STO) equation is hereby investigated with the aid of symbolic computation. A newly developed simplified bilinear method is described for the solution of considered equation. Without any constraints on the coefficient functions, multiple kink solutions are obtained. Parametric analysis is carried out in order to analyze the effects of the coefficient functions on the stabilities and propagation characteristics of the solitonic waves.

Keywords: Hirota bilinear method, multiple kink solution, Sharma-Tasso-Olver equation, inhomogeneity of media

Procedia PDF Downloads 312
2 Methods for Solving Identification Problems

Authors: Fadi Awawdeh


In this work, we highlight the key concepts in using semigroup theory as a methodology used to construct efficient formulas for solving inverse problems. The proposed method depends on some results concerning integral equations. The experimental results show the potential and limitations of the method and imply directions for future work.

Keywords: Scientific Computing, identification problems, semigroup theory, methods for inverse problems

Procedia PDF Downloads 356
1 Symbolic Computation for the Multi-Soliton Solutions of a Class of Fifth-Order Evolution Equations

Authors: Rafat Alshorman, Fadi Awawdeh


By employing a simplified bilinear method, a class of generalized fifth-order KdV (gfKdV) equations which arise in nonlinear lattice, plasma physics and ocean dynamics are investigated. With the aid of symbolic computation, both solitary wave solutions and multiple-soliton solutions are obtained. These new exact solutions will extend previous results and help us explain the properties of nonlinear solitary waves in many physical models in shallow water. Parametric analysis is carried out in order to illustrate that the soliton amplitude, width and velocity are affected by the coefficient parameters in the equation.

Keywords: multiple soliton solutions, fifth-order evolution equations, Cole-Hopf transformation, Hirota bilinear method

Procedia PDF Downloads 193