scholarly journals Conditional Invariance and Exact Solutions of a Nonlinear System

1997 ◽  
Vol 4 (1-2) ◽  
pp. 114-116
Author(s):  
Pavlo Myronyk ◽  
Natalia Bubenchikova
Keyword(s):  
Nonlinear System ◽  
Exact Solutions ◽  
Conditional Invariance

scholarly journals Multiple-soliton and Periodic Solutions to Space-time Fractional Whitham-Broer-Kaup Equations

2021 ◽  
Author(s):  
Hang Xu ◽  
Jifeng Cui
Keyword(s):  
Nonlinear System ◽  
Exact Solutions ◽  
Periodic Solutions ◽  
Nonlinear Wave ◽  
Fractional Order ◽  
Space Time ◽  
Wave System ◽  
Time And Space ◽  
Solitary Solutions ◽  
Nonlinear Wave System

Abstract In this paper, the space-time fractional Whitham-Broer-Kaup equations are investigated. By means of new fractional scaling transformations, the fractional nonlinear system of different time and space orders is transformed to the integer one. The multiple solitary solutions and periodic solutions are obtained respectively. All those solutions are given exactly by introducing new scaling transformations, which makes our study is unique and different from most existing studies. It is expected that exact solutions for nonlinear wave system of fractional order can be handled in the similar way.

New exact solutions for coupled nonlinear system of ion sound and Langmuir waves

2019 ◽  
Vol 94 (6) ◽  
pp. 885-894 ◽  
Author(s):  
M Shakeel ◽  
M A Iqbal ◽  
Q Din ◽  
Q M Hassan ◽  
K Ayub
Keyword(s):  
Nonlinear System ◽  
Exact Solutions ◽  
Langmuir Waves ◽  
New Exact Solutions
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