Cnoidal wave solutions for a class of fifth-order KdV equations

2005 ◽  
Vol 70 (4) ◽  
pp. 221-226 ◽  
Author(s):  
A.H. Khater ◽  
M.M. Hassan ◽  
R.S. Temsah
Keyword(s):  
Cnoidal Wave ◽  
Kdv Equations ◽  
Wave Solutions ◽  
Fifth Order

scholarly journals Stability Analysis for Travelling Wave Solutions of the Olver and Fifth-Order KdV Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
A. R. Seadawy ◽  
W. Amer ◽  
A. Sayed
Keyword(s):  
Water Waves ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Travelling Wave ◽  
Nonlinear Evolution Equations ◽  
Shallow Water Waves ◽  
Kdv Equations ◽  
Wave Solutions ◽  
All Solutions ◽  
Fifth Order

The Olver equation is governing a unidirectional model for describing long and small amplitude waves in shallow water waves. The solitary wave solutions of the Olver and fifth-order KdV equations can be obtained by using extended tanh and sech-tanh methods. The present results are describing the generation and evolution of such waves, their interactions, and their stability. Moreover, the methods can be applied to a wide class of nonlinear evolution equations. All solutions are exact and stable and have applications in physics.

A high-order cnoidal wave theory

1979 ◽  
Vol 94 (1) ◽  
pp. 129-161 ◽  
Author(s):  
J. D. Fenton
Keyword(s):  
Shallow Water ◽  
Wave Height ◽  
Water Depth ◽  
Wave Theory ◽  
High Order ◽  
Stokes Wave ◽  
Cnoidal Wave ◽  
Expansion Parameter ◽  
Wave Solutions ◽  
Fifth Order

A method is outlined by which high-order solutions are obtained for steadily progressing shallow water waves. It is shown that a suitable expansion parameter for these cnoidal wave solutions is the dimensionless wave height divided by the parameter m of the cn functions: this explicitly shows the limitation of the theory to waves in relatively shallow water. The corresponding deep water limitation for Stokes waves is analysed and a modified expansion parameter suggested.Cnoidal wave solutions to fifth order are given so that a steady wave problem with known water depth, wave height and wave period or length may be solved to give expressions for the wave profile and fluid velocities, as well as integral quantities such as wave power and radiation stress. These series solutions seem to exhibit asymptotic behaviour such that there is no gain in including terms beyond fifth order. Results from the present theory are compared with exact numerical results and with experiment. It is concluded that the fifth-order cnoidal theory should be used in preference to fifth-order Stokes wave theory for wavelengths greater than eight times the water depth, when it gives quite accurate results.

scholarly journals Analysing the nature of plasma and blood flow using exact roving wave solutions of fifth order rove-time equation

2021 ◽  
Vol 1145 (1) ◽  
pp. 012065
Author(s):  
R Senjudarvannan ◽  
A Revathi ◽  
R Priyadharsini ◽  
N P Sasikumar ◽  
K Banupriya ◽  
...  
Keyword(s):  
Blood Flow ◽  
Wave Solutions ◽  
Fifth Order

Application of the Exponential Rational Function Method to Some Fractional Soliton Equations

2020 ◽  
pp. 13-32
Author(s):  
Mustafa Ekici ◽  
Metin Ünal
Keyword(s):  
Differential Equations ◽  
Rational Function ◽  
Function Method ◽  
Space Time ◽  
Fractional Equations ◽  
New Exact Solutions ◽  
Kdv Equations ◽  
Fractional Differential ◽  
Exponential Rational Function Method ◽  
Fifth Order

In this chapter, the authors study the exponential rational function method to find new exact solutions for the time-fractional fifth-order Sawada-Kotera equation, the space-time fractional Whitham-Broer-Kaup equations, and the space-time fractional generalized Hirota-Satsuma coupled KdV equations. These fractional differential equations are converted into ordinary differential equations by using the fractional complex transform. The fractional derivatives are defined in the sense of Jumarie's modified Riemann-Liouville. The proposed method is direct and effective for solving different kind of nonlinear fractional equations in mathematical physics.

Sign in / Sign up

Export Citation Format

Share Document