2023
DOI: 10.3390/fractalfract7020201
|View full text |Cite
|
Sign up to set email alerts
|

Bifurcations and the Exact Solutions of the Time-Space Fractional Complex Ginzburg-Landau Equation with Parabolic Law Nonlinearity

Abstract: This paper studies the bifurcations of the exact solutions for the time–space fractional complex Ginzburg–Landau equation with parabolic law nonlinearity. Interestingly, for different parameters, there are different kinds of first integrals for the corresponding traveling wave systems. Using the method of dynamical systems, which is different from the previous works, we obtain the phase portraits of the the corresponding traveling wave systems. In addition, we derive the exact parametric representations of sol… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
1

Citation Types

0
0
0

Year Published

2023
2023
2024
2024

Publication Types

Select...
5
1

Relationship

0
6

Authors

Journals

citations
Cited by 9 publications
(1 citation statement)
references
References 36 publications
0
0
0
Order By: Relevance
“…The awareness of the importance of this kind of equation has grown continually in the last decade. Many applications have become apparent: wave propagation in a complex or porous media [1], the fractional complex Ginzburg-Landau model [2], fractional order modified Duffing systems [3], the fractional order Boussinesq-Like equations occurring in physical sciences and engineering [4], symmetric regularized long-wave (SRLW) equations arising in long water flow models [5] and extended forced Korteweg-de Vries equations with variable coefficients in fluid or plasma [6]. There are many types of fractional order derivatives, i.e., confirmable fractional derivatives [7], Beta fractional derivatives [8], Caputo-Fabrizio fractional derivatives [9], Atangana-Baleanu-Riemann derivatives [10] and truncated Mfractional derivatives [11,12].…”
Section: Introductionmentioning
confidence: 99%
“…The awareness of the importance of this kind of equation has grown continually in the last decade. Many applications have become apparent: wave propagation in a complex or porous media [1], the fractional complex Ginzburg-Landau model [2], fractional order modified Duffing systems [3], the fractional order Boussinesq-Like equations occurring in physical sciences and engineering [4], symmetric regularized long-wave (SRLW) equations arising in long water flow models [5] and extended forced Korteweg-de Vries equations with variable coefficients in fluid or plasma [6]. There are many types of fractional order derivatives, i.e., confirmable fractional derivatives [7], Beta fractional derivatives [8], Caputo-Fabrizio fractional derivatives [9], Atangana-Baleanu-Riemann derivatives [10] and truncated Mfractional derivatives [11,12].…”
Section: Introductionmentioning
confidence: 99%