scholarly journals New exact solitary wave solutions for nonlinear wave equation with fifth-order strong nonlinear term constructed by hyperbolic function type of auxiliary equation

2006 ◽  
Vol 55 (1) ◽  
pp. 13
Author(s):  
Taogetusang ◽  
Sirendaoerji
Keyword(s):  
Wave Equation ◽  
Solitary Wave ◽  
Nonlinear Wave Equation ◽  
Nonlinear Term ◽  
Hyperbolic Function ◽  
Auxiliary Equation ◽  
Solitary Wave Solutions ◽  
Function Type ◽  
Wave Solutions ◽  
Fifth Order

Applications of nonlinear longitudinal wave equation in a magneto-electro-elastic circular rod and new solitary wave solutions

2019 ◽  
Vol 33 (18) ◽  
pp. 1950210 ◽  
Author(s):  
Mujahid Iqbal ◽  
Aly R. Seadawy ◽  
Dianchen Lu
Keyword(s):  
Wave Equation ◽  
Solitary Wave ◽  
Longitudinal Wave ◽  
Electrostatic Potential ◽  
Graphical Representation ◽  
Algebraic Method ◽  
Hyperbolic Function ◽  
Auxiliary Equation ◽  
Solitary Wave Solutions ◽  
Wave Solutions

In this work, we consider the nonlinear longitudinal wave equation (LWE) which involves mathematical physics with dispersal produced by the phenomena of transverse Poisson’s effect in a magneto-electro-elastic (MEE) circular rod. We use the extended form of two methods, auxiliary equation mapping and direct algebraic method to investigated the families of solitary wave solutions of one-dimensional nonlinear LWE. These new exact and solitary wave solutions are derived in the form of trigonometric function, periodic solitary wave, rational function, and elliptic function, hyperbolic function, bright and dark solitons solutions of the LWE, which represent the electrostatic potential and pressure for LWE and also the graphical representation of electrostatic potential and pressure are shown with the aid of Mathematica program.

scholarly journals New Exact Solitary Wave Solutions of a Coupled Nonlinear Wave Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
XiaoHua Liu ◽  
CaiXia He
Keyword(s):  
Wave Equation ◽  
Solitary Wave ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Sufficient Conditions ◽  
Periodic Wave ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
Undetermined Coefficient ◽  
Planar Dynamical Systems

By using the theory of planar dynamical systems to a coupled nonlinear wave equation, the existence of bell-shaped solitary wave solutions, kink-shaped solitary wave solutions, and periodic wave solutions is obtained. Under the different parametric values, various sufficient conditions to guarantee the existence of the above solutions are given. With the help of three different undetermined coefficient methods, we investigated the new exact explicit expression of all three bell-shaped solitary wave solutions and one kink solitary wave solutions with nonzero asymptotic value for a coupled nonlinear wave equation. The solutions cannot be deduced from the former references.

scholarly journals Exact Solutions of a High-Order Nonlinear Wave Equation of Korteweg-de Vries Type under Newly Solvable Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Weiguo Rui
Keyword(s):  
Wave Equation ◽  
Solitary Wave ◽  
Exact Solutions ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
High Order ◽  
Solitary Wave Solutions ◽  
Wave Solutions

By using the integral bifurcation method together with factoring technique, we study a water wave model, a high-order nonlinear wave equation of KdV type under some newly solvable conditions. Based on our previous research works, some exact traveling wave solutions such as broken-soliton solutions, periodic wave solutions of blow-up type, smooth solitary wave solutions, and nonsmooth peakon solutions within more extensive parameter ranges are obtained. In particular, a series of smooth solitary wave solutions and nonsmooth peakon solutions are obtained. In order to show the properties of these exact solutions visually, we plot the graphs of some representative traveling wave solutions.

Computational wave solutions of generalized higher-order nonlinear Boussinesq dynamical wave equation

2019 ◽  
Vol 34 (40) ◽  
pp. 1950338 ◽  
Author(s):  
Aly R. Seadawy ◽  
David Yaro ◽  
Dianchen Lu
Keyword(s):  
Wave Equation ◽  
Solitary Wave ◽  
Boussinesq Equation ◽  
Nonlinear Partial Differential Equations ◽  
Solitary Wave Solutions ◽  
The Third ◽  
Wave Solutions ◽  
Order Nonlinear Equation ◽  
Fifth Order ◽  
Nonlinear Solutions

A Riccati equation rational expansion (RERE) method is implemented to attain solutions of nonlinear partial differential equations (NLPDEs). Subsequently, the technique is used to attain families or sets of nonlinear solutions for the third extended fifth-order nonlinear equation and the generalized (2 + 1)-dimensional Boussinesq equation. By the use of the RERE method, exciting and new forms of solution such as rational solitary wave solutions, solitary wave solutions and periodic solitary wave solutions are obtained. Some of the solutions are demonstrated graphically with specific values assigned to the parameters. It is worth noting that the application of this method is very effective and reliable.

PERIODIC WAVE SOLUTIONS FOR POCHHAMMER–CHREE EQUATION WITH FIVE ORDER NONLINEAR TERM AND THEIR RELATIONSHIP WITH SOLITARY WAVE SOLUTIONS

2010 ◽  
Vol 24 (19) ◽  
pp. 3769-3783 ◽  
Author(s):  
WEIGUO ZHANG ◽  
YAN ZHAO ◽  
GANG LIU ◽  
TONGKE NING
Keyword(s):  
Solitary Wave ◽  
Nonlinear Term ◽  
Periodic Wave ◽  
Jacobi Elliptic Function ◽  
Solitary Wave Solutions ◽  
Systematic Method ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Fifth Order ◽  
The Given

In this paper, periodic wave solutions for Pochhammer–Chree equation (PC-equation) with fifth order nonlinear term and their relationship with solitary wave solutions are studied. By designing innovative structure of solution, sixteen bounded periodic wave solutions in fractional form of Jacobi elliptic function (JEF) for PC-equation are given. Furthermore, global phase figure in the plane of the traveling solution for the PC-equation are obtained through dynamic systematic method, we indicate the region in the phase where the given sixteen solutions for PC-equation belong to. We find that two couples of these solutions change into two bell profile solitary wave solutions as k → 1 and four solutions change into four periodic wave solutions in fractional form of cosine function as k → 0. Finally, four figures are shown to describe the evolvement from periodic wave solutions to bell profile solitary wave solutions as k → 1.

Bifurcations and Single Peak Solitary Wave Solutions of an Integrable Nonlinear Wave Equation

2016 ◽  
Vol 8 (6) ◽  
pp. 1084-1098
Author(s):  
Wei Wang ◽  
Chunhai Li ◽  
Wenjing Zhu
Keyword(s):  
Wave Equation ◽  
Solitary Wave ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Soliton Solutions ◽  
Single Peak ◽  
Dynamical System Theory ◽  
Solitary Wave Solutions ◽  
Analytical Technique ◽  
Wave Solutions

AbstractDynamical system theory is applied to the integrable nonlinear wave equation ut±(u3–u2)x+(u3)xxx=0. We obtain the single peak solitary wave solutions and compacton solutions of the equation. Regular compacton solution of the equation correspond to the case of wave speed c=0. In the case of c≠0, we find smooth soliton solutions. The influence of parameters of the traveling wave solutions is explored by using the phase portrait analytical technique. Asymptotic analysis and numerical simulations are provided for these soliton solutions of the nonlinear wave equation.

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