scholarly journals Physical properties for bidirectional wave solutions to a generalized fifth-order equation with third-order time-dispersion term

2021 ◽  
pp. 104577
Author(s):  
Marwan Alquran
Keyword(s):  
Physical Properties ◽  
Order Equation ◽  
Third Order ◽  
Wave Solutions ◽  
Time Dispersion ◽  
Fifth Order ◽  
Dispersion Term

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 Rogue Wave Solutions and Generalized Darboux Transformation for an Inhomogeneous Fifth-Order Nonlinear Schrödinger Equation

2017 ◽  
Vol 2017 ◽  
pp. 1-13
Author(s):  
N. Song ◽  
W. Zhang ◽  
P. Wang ◽  
Y. K. Xue
Keyword(s):  
Darboux Transformation ◽  
Rogue Wave ◽  
Rogue Waves ◽  
Third Order ◽  
First Order ◽  
The Third ◽  
Wave Solutions ◽  
Generalized Darboux Transformation ◽  
Rogue Wave Solutions ◽  
Fifth Order

The rogue wave solutions are discussed for an inhomogeneous fifth-order nonlinear Schrödinger equation, which describes the dynamics of a site-dependent Heisenberg ferromagnetic spin chain. Using the Darboux matrix, the generalized Darboux transformation is constructed and a recursive formula is derived. Based on the transformation, the first-order to the third-order rogue wave solutions are obtained. Then, the nonlinear dynamics of the first-order to the third-order rogue waves are studied on the basis of some free parameters. Several new structures of the rogue waves are found using numerical simulation. The conclusions will be a supportive tool to study the rogue waves better.

On a nonlinear third-order equation

2017 ◽  
Vol 102 (1-2) ◽  
pp. 3-11 ◽  
Author(s):  
A. I. Aristov
Keyword(s):  
Order Equation ◽  
Third Order

Abundant rogue wave solutions for the (2 + 1)-dimensional generalized Korteweg–de Vries equation

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Huanhuan Lu ◽  
Yufeng Zhang
Keyword(s):  
Vries Equation ◽  
Rogue Wave ◽  
Rogue Waves ◽  
Third Order ◽  
First Order ◽  
Wave Solutions ◽  
De Vries ◽  
Rogue Wave Solutions ◽  
Bilinear Formulation ◽  
Hirota Bilinear

AbstractIn this paper, we analyse two types of rogue wave solutions generated from two improved ansatzs, to the (2 + 1)-dimensional generalized Korteweg–de Vries equation. With symbolic computation, the first-order rogue waves, second-order rogue waves, third-order rogue waves are generated directly from the first ansatz. Based on the Hirota bilinear formulation, another type of one-rogue waves and two-rogue waves can be obtained from the second ansatz. In addition, the dynamic behaviours of obtained rogue wave solutions are illustrated graphically.

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
Sign in / Sign up

Export Citation Format

Share Document