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A Streamlined Analytical Approach for Exact Solutions and Chaotic Dynamics in Two Higher-Dimensional Nonlinear Models.

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Title: A Streamlined Analytical Approach for Exact Solutions and Chaotic Dynamics in Two Higher-Dimensional Nonlinear Models.
Authors: Shi, Yapeng1 (AUTHOR), Feng, Yuqiang1 (AUTHOR), Yu, Jicheng2 (AUTHOR) yjicheng@126.com
Source: International Journal of Bifurcation & Chaos in Applied Sciences & Engineering. Oct2026, Vol. 36 Issue 13, p1-17. 17p.
Subject Terms: *Nonlinear evolution equations, *Chaos theory, *Lyapunov exponents, *Solitons, *Nonlinear wave equations, *Analytical solutions
Abstract: This paper employs a concise method as a streamlined analytical framework for deriving exact analytical solutions with free parameters for the higher-dimensional ZK-BBM equation and the (2 + 1) -dimensional Bogoyavlenskii system. While structurally related to traditional ansatz-based techniques, this approach reduces the reliance on predefined auxiliary equations or extensive symbolic computation by naturally deducing the governing linear ordinary differential equations during the algebraic balancing process. This offers a direct and manually verifiable derivation mechanism. A set of exact analytical solutions, including bell-shaped bright and kink solitons, are obtained and physically characterized through three-dimensional graphical representations. Dynamical analysis further reveals that these analytical solutions correspond geometrically to the homoclinic or heteroclinic orbits of the unperturbed systems, serving as baseline states for investigating nonlinear wave evolution. By introducing periodic external perturbations, the sensitivity, the coexistence of invariant orbits, and the chaotic behaviors of the corresponding two-dimensional dynamical systems are systematically investigated. The finite-time maximum Lyapunov exponent is used as a quantitative criterion to distinguish between regular quasi-periodic regimes and chaotic states. These results provide detailed insights into complex wave phenomena and the topological dynamics of higher-dimensional nonlinear evolution equations. [ABSTRACT FROM AUTHOR]
Database: Academic Search Index
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DbLabel: Academic Search Index
An: 195723063
RelevancyScore: 1452
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PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 1452.43029785156
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  Data: A Streamlined Analytical Approach for Exact Solutions and Chaotic Dynamics in Two Higher-Dimensional Nonlinear Models.
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  Data: <searchLink fieldCode="AR" term="%22Shi%2C+Yapeng%22">Shi, Yapeng</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Feng%2C+Yuqiang%22">Feng, Yuqiang</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Yu%2C+Jicheng%22">Yu, Jicheng</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> yjicheng@126.com</i>
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  Data: <searchLink fieldCode="JN" term="%22International+Journal+of+Bifurcation+%26+Chaos+in+Applied+Sciences+%26+Engineering%22">International Journal of Bifurcation & Chaos in Applied Sciences & Engineering</searchLink>. Oct2026, Vol. 36 Issue 13, p1-17. 17p.
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  Data: *<searchLink fieldCode="DE" term="%22Nonlinear+evolution+equations%22">Nonlinear evolution equations</searchLink><br />*<searchLink fieldCode="DE" term="%22Chaos+theory%22">Chaos theory</searchLink><br />*<searchLink fieldCode="DE" term="%22Lyapunov+exponents%22">Lyapunov exponents</searchLink><br />*<searchLink fieldCode="DE" term="%22Solitons%22">Solitons</searchLink><br />*<searchLink fieldCode="DE" term="%22Nonlinear+wave+equations%22">Nonlinear wave equations</searchLink><br />*<searchLink fieldCode="DE" term="%22Analytical+solutions%22">Analytical solutions</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: This paper employs a concise method as a streamlined analytical framework for deriving exact analytical solutions with free parameters for the higher-dimensional ZK-BBM equation and the (2 + 1) -dimensional Bogoyavlenskii system. While structurally related to traditional ansatz-based techniques, this approach reduces the reliance on predefined auxiliary equations or extensive symbolic computation by naturally deducing the governing linear ordinary differential equations during the algebraic balancing process. This offers a direct and manually verifiable derivation mechanism. A set of exact analytical solutions, including bell-shaped bright and kink solitons, are obtained and physically characterized through three-dimensional graphical representations. Dynamical analysis further reveals that these analytical solutions correspond geometrically to the homoclinic or heteroclinic orbits of the unperturbed systems, serving as baseline states for investigating nonlinear wave evolution. By introducing periodic external perturbations, the sensitivity, the coexistence of invariant orbits, and the chaotic behaviors of the corresponding two-dimensional dynamical systems are systematically investigated. The finite-time maximum Lyapunov exponent is used as a quantitative criterion to distinguish between regular quasi-periodic regimes and chaotic states. These results provide detailed insights into complex wave phenomena and the topological dynamics of higher-dimensional nonlinear evolution equations. [ABSTRACT FROM AUTHOR]
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RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1142/S0218127426501804
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 17
        StartPage: 1
    Subjects:
      – SubjectFull: Nonlinear evolution equations
        Type: general
      – SubjectFull: Chaos theory
        Type: general
      – SubjectFull: Lyapunov exponents
        Type: general
      – SubjectFull: Solitons
        Type: general
      – SubjectFull: Nonlinear wave equations
        Type: general
      – SubjectFull: Analytical solutions
        Type: general
    Titles:
      – TitleFull: A Streamlined Analytical Approach for Exact Solutions and Chaotic Dynamics in Two Higher-Dimensional Nonlinear Models.
        Type: main
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          Name:
            NameFull: Shi, Yapeng
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          Name:
            NameFull: Feng, Yuqiang
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          Name:
            NameFull: Yu, Jicheng
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          Dates:
            – D: 01
              M: 10
              Text: Oct2026
              Type: published
              Y: 2026
          Identifiers:
            – Type: issn-print
              Value: 02181274
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            – Type: volume
              Value: 36
            – Type: issue
              Value: 13
          Titles:
            – TitleFull: International Journal of Bifurcation & Chaos in Applied Sciences & Engineering
              Type: main
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