Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 4

Hirota bilinear method Related Abstracts

4 Symbolic Computation for the Multi-Soliton Solutions of a Class of Fifth-Order Evolution Equations

Authors: Rafat Alshorman, Fadi Awawdeh

Abstract:

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

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

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

Abstract:

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

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2 Symbolic Computation on Variable-Coefficient Non-Linear Dispersive Wave Equations

Authors: Edris Rawashdeh, I. Abu-Falahah, H. M. Jaradat

Abstract:

The variable-coefficient non-linear dispersive wave equation is investigated with the aid of symbolic computation. By virtue of a newly developed simplified bilinear method, multi-soliton solutions for such an equation have been derived. Effects of the inhomogeneities of media and nonuniformities of boundaries, depicted by the variable coefficients, on the soliton behavior are discussed with the aid of the characteristic curve method and graphical analysis.

Keywords: Symbolic Computation, Hirota bilinear method, dispersive wave equations, multiple soliton solution

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1 Multiple-Lump-Type Solutions of the 2D Toda Equation

Authors: Jian-Ping Yu, Wen-Xiu Ma, Yong-Li Sun, Chaudry Masood Khalique

Abstract:

In this paper, a 2d Toda equation is studied, which is a classical integrable system and plays a vital role in mathematics, physics and other areas. New lump-type solution is constructed by using the Hirota bilinear method. One interesting feature of this research is that this lump-type solutions possesses two types of multiple-lump-type waves, which are one- and two-lump-type waves. Moreover, the corresponding 3d plots, density plots and contour plots are given to show the dynamical features of the obtained multiple-lump-type solutions.

Keywords: Hirota bilinear method, Lump-type solution, multiple-lump-type solution

Procedia PDF Downloads 60