scholarly journals Qualitative Analysis and Traveling wave Solutions for the Nonlinear Convection Equations with Absorption

2020 ◽  
Vol 1591 ◽  
pp. 012052
Author(s):  
Bashayir N. Abed ◽  
Salam J. Majeed ◽  
Habeeb A. Aal-Rkhais
Keyword(s):  
Qualitative Analysis ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Nonlinear Convection ◽  
Wave Solutions

Exact Cuspon and Compactons of the Novikov Equation

2014 ◽  
Vol 24 (03) ◽  
pp. 1450037 ◽  
Author(s):  
Jibin Li
Keyword(s):  
Dynamical Systems ◽  
Qualitative Analysis ◽  
Traveling Wave ◽  
Wave Solution ◽  
Traveling Wave Solutions ◽  
Phase Portraits ◽  
Breaking Wave ◽  
Wave Solutions ◽  
Novikov Equation

In this paper, we apply the method of dynamical systems to the traveling wave solutions of the Novikov equation. Through qualitative analysis, we obtain bifurcations of phase portraits of the traveling system and exact cuspon wave solution, as well as a family of breaking wave solutions (compactons). We find that the corresponding traveling system of Novikov equation has no one-peakon solution.

scholarly journals LS method and qualitative analysis of traveling wave solutions of Fisher equation

2010 ◽  
Vol 59 (2) ◽  
pp. 744
Author(s):  
Li Xiang-Zheng ◽  
Zhang Wei-Guo ◽  
Yuan San-Ling
Keyword(s):  
Qualitative Analysis ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Fisher Equation ◽  
Wave Solutions

TRAVELING WAVE SOLUTIONS OF THE GREEN–NAGHDI SYSTEM

2013 ◽  
Vol 23 (05) ◽  
pp. 1350087 ◽  
Author(s):  
SHENGFU DENG ◽  
BOLING GUO ◽  
TINGCHUN WANG
Keyword(s):  
Qualitative Analysis ◽  
Traveling Wave ◽  
Autonomous Systems ◽  
Traveling Wave Solutions ◽  
Phase Portraits ◽  
Equivalent System ◽  
Wave Solutions ◽  
Analysis Methods

We investigate the traveling wave solutions of the Green–Naghdi system. Using the qualitative analysis methods of planar autonomous systems, we show not only its phase portraits but also the exact expressions of some bounded wave solutions. These results are a complement of the work by Deng et al. [2011], which studied the traveling wave solutions of its equivalent system under some conditions.

SOME TRAVELING WAVE SOLITONS OF THE GREEN–NAGHDI SYSTEM

2011 ◽  
Vol 21 (02) ◽  
pp. 575-585 ◽  
Author(s):  
SHENGFU DENG ◽  
BOLING GUO ◽  
TINGCHUN WANG
Keyword(s):  
Qualitative Analysis ◽  
Traveling Wave ◽  
Autonomous Systems ◽  
Traveling Wave Solutions ◽  
Periodic Wave ◽  
Phase Portraits ◽  
Equivalent System ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Soliton Wave Solutions

The traveling wave solutions for an equivalent system of the Green–Naghdi system are considered. The qualitative analysis methods of planar autonomous systems yield their phase portraits. The exact expressions of smooth soliton wave solutions, cusp soliton wave solutions, smooth periodic wave solutions and periodic cusp wave solutions are obtained. Some numerical simulations of these solutions are also given. These reveal some new properties of the Green–Naghdi system.

Qualitative analysis and new soliton solutions for the coupled nonlinear Schrödinger type equations

2021 ◽  
Author(s):  
M. E. Elbrolosy
Keyword(s):  
Qualitative Analysis ◽  
Traveling Wave ◽  
Bifurcation Theory ◽  
Soliton Solutions ◽  
Traveling Wave Solutions ◽  
Singular Solutions ◽  
Wave System ◽  
Nonlinear Schrödinger ◽  
Perturbed System ◽  
Wave Solutions

Abstract This work is interested in constructing new traveling wave solutions for the coupled nonlinear Schrödinger type equations. It is shown that the equations can be converted to a conservative Hamiltonian traveling wave system. By using the bifurcation theory and Qualitative analysis, we assign the permitted intervals of real propagation. The conserved quantity is utilized to construct sixteen traveling wave solutions; four periodic, two kink, and ten singular solutions. The periodic and kink solutions are analyzed numerically considering the affect of varying each parameter keeping the others fixed. The degeneracy of the solutions discussed through the transmission of the orbits illustrates the consistency of the solutions. The 3D and 2D graphical representations for solutions are presented. Finally, we investigate numerically the quasi-periodic behavior for the perturbed system after inserting a periodic term.

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