scholarly journals Construction of New Exact Solutions for the (3 + 1)-Dimensional Burgers System

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Zitian Li
Keyword(s):  
Solitary Wave ◽  
Exact Solutions ◽  
Separation Method ◽  
Solitary Wave Solutions ◽  
Variable Separation ◽  
New Exact Solutions ◽  
Wave Solutions ◽  
Kink Wave ◽  
Variable Separation Method ◽  
Burgers System

By means of a variable separation method and a generalized direct ansätz function approach, new exact solutions including cross kink-wave solutions, doubly periodic kinky-wave solutions, and breather type of two-solitary wave solutions for the (3 + 1)-dimensional Burgers system are obtained. Moreover, the mechanical features are also investigated.

Solitary Wave and Periodic Wave Solutions and Chaotic Behaviors in a (2+1)-Dimensional Nonlinear System

2014 ◽  
Vol 532 ◽  
pp. 346-350
Author(s):  
Xiao Xin Zhu ◽  
Song Hua Ma ◽  
Qing Bao Ren
Keyword(s):  
Solitary Wave ◽  
Solitary Wave Solution ◽  
Periodic Wave ◽  
Mapping Method ◽  
Solitary Wave Solutions ◽  
Variable Separation ◽  
Periodic Wave Solutions ◽  
New Exact Solutions ◽  
Wave Solutions ◽  
Variable Separation Method

With the help of the symbolic computation system Maple and an improved mapping method and a variable separation method, a series of new exact solutions (including solitary wave solutions and periodic wave solutions) to the (2+1)-dimensional general Nizhnik-Novikov-Veselov (GNNV) system is derived. Based on the derived solitary wave solution, we obtain some chaotic patterns.

Investigation of (G'/G)-Expansion Method and Exact Solutions for the (2+1)-Dimensional Calogero-Bogoyavlenskii-Schiff System

2013 ◽  
Vol 432 ◽  
pp. 235-239
Author(s):  
Gen Hai Xu ◽  
Song Hua Ma ◽  
Jian Ping Fang
Keyword(s):  
Solitary Wave ◽  
Exact Solutions ◽  
Expansion Method ◽  
Periodic Wave ◽  
Solitary Wave Solutions ◽  
Variable Separation ◽  
Periodic Wave Solutions ◽  
New Family ◽  
Wave Solutions ◽  
Variable Separation Method

With the help of the symbolic computation system Maple and the (G'/G)-expansion method and a linear variable separation method, a new family of exact solutions (including solitary wave solutions,periodic wave solutions and rational function solutions) of the (2+1)-dimensional Calogero-Bogoyavlenskii-Schiff system (2DCBS) is derived.

scholarly journals New Exact Solutions for High Dispersive Cubic-Quintic Nonlinear Schrödinger Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Yongan Xie ◽  
Shengqiang Tang
Keyword(s):  
Solitary Wave ◽  
Exact Solutions ◽  
Bifurcation Theory ◽  
Solitary Wave Solutions ◽  
Nonlinear Schrödinger ◽  
Light Pulses ◽  
New Exact Solutions ◽  
Wave Solutions ◽  
First Time ◽  
Quintic Nonlinear Schrödinger Equation

We study a class of high dispersive cubic-quintic nonlinear Schrödinger equations, which describes the propagation of femtosecond light pulses in a medium that exhibits a parabolic nonlinearity law. Applying bifurcation theory of dynamical systems and the Fan sub-equations method, more types of exact solutions, particularly solitary wave solutions, are obtained for the first time.

scholarly journals New Solitary and Periodic Wave Solutions of (n + 1)-Dimensional Fractional Order Equations Modeling Fluid Dynamics

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2017
Author(s):  
Sadullah Bulut ◽  
Mesut Karabacak ◽  
Hijaz Ahmad ◽  
Sameh Askar
Keyword(s):  
Solitary Wave ◽  
Fractional Derivative ◽  
Exact Solutions ◽  
Wave Model ◽  
Expansion Method ◽  
Periodic Wave ◽  
Solitary Wave Solutions ◽  
New Exact Solutions ◽  
Wave Solutions ◽  
Symmetry Properties

In this study, first, fractional derivative definitions in the literature are examined and their disadvantages are explained in detail. Then, it seems appropriate to apply the (G′G)-expansion method under Atangana’s definition of β-conformable fractional derivative to obtain the exact solutions of the space–time fractional differential equations, which have attracted the attention of many researchers recently. The method is applied to different versions of (n+1)-dimensional Kadomtsev–Petviashvili equations and new exact solutions of these equations depending on the β parameter are acquired. If the parameter values in the new solutions obtained are selected appropriately, 2D and 3D graphs are plotted. Thus, the decay and symmetry properties of solitary wave solutions in a nonlocal shallow water wave model are investigated. It is also shown that all such solitary wave solutions are symmetrical on both sides of the apex. In addition, a close relationship is established between symmetric and propagated wave solutions.

scholarly journals New exact solutions of the(2+1)-dimensional Broer-Kaup equation by the consistent Riccati expansion method

2017 ◽  
Vol 21 (4) ◽  
pp. 1783-1788 ◽  
Author(s):  
Ying Jiang ◽  
Da-Quan Xian ◽  
Zheng-De Dai
Keyword(s):  
Solitary Wave ◽  
Exact Solutions ◽  
Expansion Method ◽  
High Dimensional ◽  
Solitary Wave Solutions ◽  
New Exact Solutions ◽  
Dynamical Behaviors ◽  
Wave Solutions ◽  
Linear Waves ◽  
Consistent Riccati Expansion

In this work, we study the (2+1)-D Broer-Kaup equation. The composite periodic breather wave, the exact composite kink breather wave and the solitary wave solutions are obtained by using the coupled degradation technique and the consistent Riccati expansion method. These results may help us to investigate some complex dynamical behaviors and the interaction between composite non-linear waves in high dimensional models

Study of the Exact Solutions and Chaotic Behaviors in a (2+1)-Dimensional Nonlinear System

2013 ◽  
Vol 340 ◽  
pp. 755-759
Author(s):  
Song Hua Ma
Keyword(s):  
Solitary Wave ◽  
Exact Solutions ◽  
Water Wave ◽  
Solitary Wave Solution ◽  
Periodic Wave ◽  
Solitary Wave Solutions ◽  
Variable Separation ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Variable Separation Approach

With the help of the symbolic computation system Maple and the (G'/G)-expansion approach and a special variable separation approach, a series of exact solutions (including solitary wave solutions, periodic wave solutions and rational function solutions) of the (2+1)-dimensional modified dispersive water-wave (MDWW) system is derived. Based on the derived solitary wave solution, some novel domino solutions and chaotic patterns are investigated.

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

2008 ◽  
Vol 63 (10-11) ◽  
pp. 641-645
Author(s):  
Jiang-Bo Li ◽  
Chun-Long Zheng ◽  
Song-Hua Ma
Keyword(s):  
Solitary Wave ◽  
Periodic Wave ◽  
Solitary Wave Solutions ◽  
Variable Separation ◽  
Periodic Wave Solutions ◽  
New Exact Solutions ◽  
Wave Solutions ◽  
Complex Wave ◽  
Special Complex ◽  
Variable Separation Approach

Starting from an improved mapping approach and a linear variable separation approach, new families of variable separated solutions (including solitary wave solutions, periodic wave solutions and rational function solutions) with arbitrary functions for the (2+1)-dimensional asymmetric Nizhnik- Novikov-Veselov (ANNV) system are derived. Based on the derived solutions, we obtain some special complex wave excitations.

scholarly journals Exact Traveling Wave Solutions for a Nonlinear Evolution Equation of Generalized Tzitzéica-Dodd-Bullough-Mikhailov Type

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Weiguo Rui
Keyword(s):  
Solitary Wave ◽  
Exact Solutions ◽  
Traveling Wave ◽  
Blow Up ◽  
Traveling Wave Solutions ◽  
Solitary Wave Solutions ◽  
Bifurcation Method ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions ◽  
Kink Wave

By using the integral bifurcation method, a generalized Tzitzéica-Dodd-Bullough-Mikhailov (TDBM) equation is studied. Under different parameters, we investigated different kinds of exact traveling wave solutions of this generalized TDBM equation. Many singular traveling wave solutions with blow-up form and broken form, such as periodic blow-up wave solutions, solitary wave solutions of blow-up form, broken solitary wave solutions, broken kink wave solutions, and some unboundary wave solutions, are obtained. In order to visually show dynamical behaviors of these exact solutions, we plot graphs of profiles for some exact solutions and discuss their dynamical properties.

scholarly journals New Exact Solutions for the(2+1)-Dimensional Broer-Kaup-Kupershmidt Equations

2010 ◽  
Vol 2010 ◽  
pp. 1-9 ◽  
Author(s):  
Ming Song ◽  
Shaoyong Li ◽  
Jun Cao
Keyword(s):  
Dynamical Systems ◽  
Solitary Wave ◽  
Exact Solutions ◽  
Blow Up ◽  
Qualitative Theory ◽  
Solitary Wave Solutions ◽  
Bifurcation Method ◽  
New Exact Solutions ◽  
Wave Solutions ◽  
Explicit Expressions

We investigate the(2+1)-dimensional Broer-Kaup-Kupershmidt equations. Some explicit expressions of solutions for the equations are obtained by using the bifurcation method and qualitative theory of dynamical systems. These solutions contain kink-shaped solutions, blow-up solutions, periodic blow-up solutions, and solitary wave solutions. Some previous results are extended.

scholarly journals New Exact Solutions to the KdV-Burgers-Kuramoto Equation with the Exp-Function Method

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Jae-Myoung Kim ◽  
Changbum Chun
Keyword(s):  
Solitary Wave ◽  
Exact Solutions ◽  
Function Method ◽  
Expansion Method ◽  
Solitary Wave Solutions ◽  
New Exact Solutions ◽  
Wave Solutions ◽  
Truncated Painlevé Expansion

Based on the characteristics of the truncated Painlevé expansion method and the Exp-function method, new generalized solitary wave solutions are constructed for the KdV-Burgers-Kuramoto equation, which cannot be directly constructed from the Exp-function method. This work highlights the power of the Exp-function method in providing generalized solitary wave solutions of different physical structures.

Sign in / Sign up

Export Citation Format

Share Document