A Unified Analysis of Exact Traveling Wave Solutions for the Fractional-Order and Integer-Order Biswas–Milovic Equation: Via Bifurcation Theory of Dynamical System

This paper presents a unified method to investigate exact traveling wave solutions of the nonlinear fractional-order and integer-order partial differential equations. We use the conformable fractional derivatives. The method is based on the bifurcation theory of planar dynamical systems. To show the...

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Bibliographic Details
Published in:Qualitative theory of dynamical systems Vol. 19; no. 1
Main Authors: Zhang, Bei, Zhu, Wenjing, Xia, Yonghui, Bai, Yuzhen
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.04.2020
Springer Nature B.V
Subjects:
Bifurcation theory
Difference and Functional Equations
Dynamical systems
Dynamical Systems and Ergodic Theory
Integers
Mathematical analysis
Mathematics
Mathematics and Statistics
Nonlinear equations
Partial differential equations
System effectiveness
Traveling waves
Bifurcation
Periodic wave solution
Solitary wave solution
Traveling wave solution
Kink wave solution
ISSN:1575-5460, 1662-3592
Online Access:Get full text
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Summary:This paper presents a unified method to investigate exact traveling wave solutions of the nonlinear fractional-order and integer-order partial differential equations. We use the conformable fractional derivatives. The method is based on the bifurcation theory of planar dynamical systems. To show the effectiveness of this method, we choose Biswas–Milovic (for short, BM) equation with conformable derivative as an application. Also comparison is presented for the exact traveling wave solutions between the integer-order BM equation and fractional-order BM equation. It is believed that this approach can be extended to other nonlinear fractional-order partial differential equations.
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ISSN:1575-5460
1662-3592
DOI:10.1007/s12346-020-00352-x