Integrating the loaded KdV equation with a self-consistent source of integral type in the class of rapidly decreasing complex-valued functions

2021 ◽  
Vol 24 (2) ◽  
pp. 181-198
Author(s):  
U. A. Hoitmetov
Keyword(s):  
Kdv Equation ◽  
Integral Type ◽  
Self Consistent ◽  
Complex Valued

scholarly journals On the Integration of the matrix modified Korteweg-de Vries equation with a self-consistent source

2019 ◽  
Vol 50 (3) ◽  
pp. 281-291 ◽  
Author(s):  
G. U. Urazboev ◽  
A. K. Babadjanova
Keyword(s):  
Vries Equation ◽  
Kdv Equation ◽  
Scattering Data ◽  
Self Consistent ◽  
De Vries ◽  
The Matrix

In this work we deduce laws of the evolution of the scattering  data for the matrix Zakharov Shabat system with the potential that is the solution of the matrix modied KdV equation with a self consistent source.

Integration of the matrix KdV equation with self-consistent source

2013 ◽  
Vol 49 ◽  
pp. 21-27 ◽  
Author(s):  
N. Bondarenko ◽  
G. Freiling ◽  
G. Urazboev
Keyword(s):  
Kdv Equation ◽  
Self Consistent ◽  
The Matrix

scholarly journals Solutions and Painlevé Property for the KdV Equation with Self-Consistent Source

2018 ◽  
Vol 2018 ◽  
pp. 1-16
Author(s):  
Yali Shen ◽  
Ruoxia Yao
Keyword(s):  
Kdv Equation ◽  
Traveling Wave Solutions ◽  
Elliptic Functions ◽  
Expansion Method ◽  
Hyperbolic Function ◽  
Group Invariant ◽  
Painlevé Property ◽  
The Kdv Equation ◽  
Self Consistent ◽  
Group Invariant Solutions

In this paper, the polynomial solutions in terms of Jacobi’s elliptic functions of the KdV equation with a self-consistent source (KdV-SCS) are presented. The extended (G′/G)-expansion method is utilized to obtain exact traveling wave solutions of the KdV-SCS, which finally are expressed in terms of the hyperbolic function, the trigonometric function, and the rational function. Meanwhile we find the Lie point symmetry and Lie symmetry group and give several group-invariant solutions for the KdV-SCS. Finally, we supplement the results of the Painlevé property in our previous work and get the Bäcklund transformations of the KdV-SCS.

KdV Equation with Self-consistent Sources in Non-uniform Media

2009 ◽  
Vol 51 (6) ◽  
pp. 989-999 ◽  
Author(s):  
Hao Hong-Hai ◽  
Wang Guang-Sheng ◽  
Zhang Da-Jun
Keyword(s):  
Kdv Equation ◽  
Self Consistent

scholarly journals An Approach of Integral Equations in Complex-Valued b -Metric Space Using Commuting Self-Maps

2022 ◽  
Vol 2022 ◽  
pp. 1-19
Author(s):  
Rashad A. R. Bantan ◽  
Saif Ur Rehman ◽  
Shahid Mehmood ◽  
Waleed Almutiry ◽  
Amani Abdullah Alahmadi ◽  
...  
Keyword(s):  
Metric Space ◽  
Fixed Point Theorems ◽  
Integral Operators ◽  
Integral Type ◽  
The One ◽  
Complex Valued ◽  
Common Fixed Point Theorems ◽  
Rational Type ◽  
Type Contraction ◽  
Unique Common Fixed Point

This paper is aimed at establishing some unique common fixed point theorems in complex-valued b -metric space under the rational type contraction conditions for three self-mappings in which the one self-map is continuous. A continuous self-map is commutable with the other two self-mappings. Our results are verified by some suitable examples. Ultimately, our results have been utilized to prove the existing solution to the two Urysohn integral type equations. This application illustrates how complex-valued b -metric space can be used in other types of integral operators.

scholarly journals Rational Type Compatible Single-Valued Mappings via Unique Common Fixed Point Findings in Complex-Valued b-Metric Spaces with an Application

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Shahid Mehmood ◽  
Saif Ur Rehman ◽  
Naeem Jan ◽  
Mabrook Al-Rakhami ◽  
Abdu Gumaei
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Spaces ◽  
Continuous Functions ◽  
Integral Type ◽  
Common Solution ◽  
Main Work ◽  
Complex Valued ◽  
Rational Type ◽  
Unique Common Fixed Point

In this paper, we establish some new generalized rational type common fixed point results for compatible three self-mappings in complex-valued b-metric space, in which a one self-map is continuous. In support of our results, we present some illustrative examples to verify the validity of our main work. Moreover, we present the application of two Urysohn integral type equations (UITEs) for the existence of a common solution to support our work. The UITEs are v 1 p = ∫ k 1 k 2 Q 1 p , r , v 1 r d r + ℏ 1 p and v 2 p = ∫ k 1 k 2 Q 2 p , r , v 2 r d r + ℏ 2 p , where p ∈ k 1 , k 2 , v 1 , v 2 , ℏ 1 , ℏ 2 ∈ V , where V = C k 1 , k 2 , ℝ n is the set of all real-valued continuous functions defined on k 1 , k 2 and Q 1 , Q 2 : k 1 , k 2 × k 1 , k 2 × ℝ n ⟶ ℝ n .

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