On exact solutions of the regularized long‐wave equation: A direct approach to partially integrable equations. II. Periodic solutions

1995 ◽  
Vol 36 (7) ◽  
pp. 3506-3519 ◽  
Author(s):  
A. Parker
Keyword(s):  
Wave Equation ◽  
Exact Solutions ◽  
Periodic Solutions ◽  
Direct Approach ◽  
Integrable Equations ◽  
Long Wave ◽  
Regularized Long Wave Equation

Rosenau-KdV Equation Coupling with the Rosenau-RLW Equation: Conservation Laws and Exact Solutions

2017 ◽  
Vol 18 (6) ◽  
pp. 451-456 ◽  
Author(s):  
Ben Muatjetjeja ◽  
Abdullahi Rashid Adem
Keyword(s):  
Wave Equation ◽  
Conservation Laws ◽  
Exact Solutions ◽  
Vries Equation ◽  
Kdv Equation ◽  
Long Wave ◽  
Rlw Equation ◽  
Kudryashov Method ◽  
Regularized Long Wave Equation ◽  
De Vries

AbstractWe compute the conservation laws for the Rosenau-Kortweg de Vries equation coupling with the Regularized Long-Wave equation using Noether’s approach through a remarkable method of increasing the order of the Rosenau-KdV-RLW equation. Furthermore, exact solutions for the Rosenau- KdV-RLW equation are acquired by employing the Kudryashov method.

scholarly journals Exact Solutions of the Symmetric Regularized Long Wave Equation and the Klein-Gordon-Zakharov Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Isaiah Elvis Mhlanga ◽  
Chaudry Masood Khalique
Keyword(s):  
Wave Equation ◽  
Exact Solutions ◽  
Nonlinear Partial Differential Equations ◽  
Travelling Wave ◽  
Symmetry Approach ◽  
New Exact Solutions ◽  
Long Wave ◽  
Simplest Equation Method ◽  
Regularized Long Wave Equation ◽  
Klein Gordon

We study two nonlinear partial differential equations, namely, the symmetric regularized long wave equation and the Klein-Gordon-Zakharov equations. The Lie symmetry approach along with the simplest equation and exp-function methods are used to obtain solutions of the symmetric regularized long wave equation, while the travelling wave hypothesis approach along with the simplest equation method is utilized to obtain new exact solutions of the Klein-Gordon-Zakharov equations.

Euler operators and conservation laws of the BBM equation

1979 ◽  
Vol 85 (1) ◽  
pp. 143-160 ◽  
Author(s):  
Peter J. Olver
Keyword(s):  
Wave Equation ◽  
Conservation Laws ◽  
Calculus Of Variations ◽  
Long Wave ◽  
Regularized Long Wave Equation ◽  
Formal Calculus ◽  
Euler Operators ◽  
Bbm Equation

AbstractThe BBM or Regularized Long Wave Equation is shown to possess only three non-trivial independent conservation laws. In order to prove this result, a new theory of Euler-type operators in the formal calculus of variations will be developed in detail.

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