Travelling wave solutions of special type to third order nonlinear PDE of mathematical physics

2010 ◽  
pp. 31-68
Keyword(s):  
Mathematical Physics ◽  
Travelling Wave ◽  
Nonlinear Pde ◽  
Travelling Wave Solutions ◽  
Third Order ◽  
Wave Solutions

scholarly journals Travelling Wave Solutions of the Perturbed Wadati-Segur-Ablowitz Equation by (G'/G)-Expansion Method

2018 ◽  
Vol 6 (06) ◽  
Author(s):  
Figen Kangalgil
Keyword(s):  
Exact Solutions ◽  
Rational Functions ◽  
Expansion Method ◽  
Mathematical Physics ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
Nonlinear Physical Phenomena ◽  
Physical Phenomena

The investigation of the exact solutions of NLPDEs plays an im- portant role for the understanding of most nonlinear physical phenomena. Also, the exact solutions of this equations aid the numerical solvers to assess the correctness of their results. In this paper, (G'/G)-expansion method is pre- sented to construct exact solutions of the Perturbed Wadati-Segur-Ablowitz equation. Obtained the exact solutions are expressed by the hyperbolic, the trigonometric and the rational functions. All calculations have been made with the aid of Maple program. It is shown that the proposed algorithm is elemen- tary, e¤ective and has been used for many PDEs in mathematical physics.  

New Soliton Solutions of Chaffee-Infante Equations Using the Exp-Function Method

2010 ◽  
Vol 65 (3) ◽  
pp. 197-202 ◽  
Author(s):  
Rathinasamy Sakthivel ◽  
Changbum Chun
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Symbolic Computation ◽  
Function Method ◽  
Nonlinear Partial Differential Equations ◽  
Soliton Solutions ◽  
Mathematical Physics ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Wave Solutions

In this paper, the exp-function method is applied by using symbolic computation to construct a variety of new generalized solitonary solutions for the Chaffee-Infante equation with distinct physical structures. The results reveal that the exp-function method is suited for finding travelling wave solutions of nonlinear partial differential equations arising in mathematical physics

A Note on Exact Travelling Wave Solutions for Nonlinear PHI-Four Equation

2012 ◽  
Vol 204-208 ◽  
pp. 4569-4572
Author(s):  
Chun Huan Xiang
Keyword(s):  
Nonlinear System ◽  
Particle Physics ◽  
Dynamical Behavior ◽  
Mathematical Physics ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Hyperbolic Tangent ◽  
Wave Solutions ◽  
Tangent Method

The purpose of this work is to reveal the dynamical behavior of the nonlinear PHI-four equation, which is an interesting and very useful model in particle physics and mathematical physics. As a result, travelling wave solutions of nonlinear PHI-four equation are formally derived by employing hyperbolic tangent method in this paper. This paper shows that hyperbolic tangent method can be a powerful tool in obtaining evolution solutions of nonlinear system.

Bell-shaped soliton solutions and travelling wave solutions of the fifth-order nonlinear modified Kawahara equation

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Ali Başhan
Keyword(s):  
Soliton Solutions ◽  
Travelling Wave ◽  
Test Problems ◽  
Simple Type ◽  
Order Partial Differential Equation ◽  
Travelling Wave Solutions ◽  
Kawahara Equation ◽  
Third Order ◽  
Wave Solutions ◽  
Fifth Order

AbstractThe main aim of this work is to investigate numerical solutions of the two different types of the fifth-order modified Kawahara equation namely bell-shaped soliton solutions and travelling wave solutions that occur thereby the different type of the Korteweg–de Vries equation. For this approach, we have used an effective and simple type of finite difference method namely Crank-Nicolson scheme for time integration and third-order modified cubic B-spline-based differential quadrature method for space integration. We preferred the third-order modified cubic B-splines to solve the fifth-order partial differential equation because of by using low energy, less algebraic process and produce better results than earlier works. To display the efficiency and accuracy of the present fresh approach famous test problems namely bell-shaped single soliton that has negative amplitude and travelling wave solutions that have the both of the positive and negative amplitudes are solved and the error norms L2 and L∞ are calculated and compared with earlier works. Comparison of the error norms show that present fresh approach obtained superior results than earlier works by using same parameters. At the same time, two lowest invariants of the test problems during the simulations are calculated and reported. Besides those, relative changes of invariants are computed and reported.

scholarly journals On the conservation laws and solutions of a (2+1) dimensional KdV-mKdV equation of mathematical physics

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 211-214 ◽  
Author(s):  
Tanki Motsepa ◽  
Chaudry Masood Khalique
Keyword(s):  
Partial Differential Equations ◽  
Conservation Laws ◽  
Elliptic Functions ◽  
Mathematical Physics ◽  
Travelling Wave ◽  
Mkdv Equation ◽  
Jacobi Elliptic Functions ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
Physical Phenomena

AbstractIn this paper, we study a (2+1) dimensional KdV-mKdV equation, which models many physical phenomena of mathematical physics. This equation has two integral terms in it. By an appropriate substitution, we convert this equation into two partial differential equations, which do not have integral terms and are equivalent to the original equation. We then work with the system of two equations and obtain its exact travelling wave solutions in form of Jacobi elliptic functions. Furthermore, we employ the multiplier method to construct conservation laws for the system. Finally, we revert the results obtained into the original variables of the (2+1) dimensional KdV-mKdV equation.

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