[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content
Springer Nature Link
Log in

On compacton traveling wave solutions of Zakharov-Kuznetsov-Benjamin-Bona-Mahony (ZK-BBM) equation

  • Published:
Computational and Applied Mathematics Aims and scope Submit manuscript

Abstract

Nonlinear evolution equations are used to model various complex physical phenomena, and finding exact solutions of these equations is important for their applications. One of the important problem is that of finding traveling wave solutions in well-known nonlinear evolution systems from mathematical physics. In this paper, the differential transformation method (DTM) along with the wave-like transformation is used to develop the compacton traveling wave solution of nonlinear Zakharov-Kuznetsov-Benjamin-Bona-Mahony (ZK-BBM) equation. The multiple choices for the parameters in the partial differential equation are studied and results shows that the method is efficient to develop new compacton wave solutions of partial differential equation. We plot the exact analytical and numerical solutions for different values of parameters. These results validate the experiment results.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  • Ahmadi MB, Kiania NA (2013) Differential transformation method for solving fuzzy differential inclusions by fuzzy partitions. Int J Ind Math 5(3):237–249

    Google Scholar 

  • Ali A, Iqbal MA, Mohyud-Din ST (2016) Solitary wave solutions zakharov-kuznetsov-benjamin-bona-mahony (zk-bbm) equation. J Egypt Math Soc 24(1):44–48

    Article  MathSciNet  MATH  Google Scholar 

  • Allahviranloo T, Abbasbandy S, Salahshour S, Hakimzadeh A (2011) A new method for solving fuzzy linear differential equations. Computing 92(2):181–197

    Article  MathSciNet  MATH  Google Scholar 

  • Allahviranloo T, Kiani NA, Motamedi N (2009) Solving fuzzy differential equations by differential transformation method. Inform Sci 179(7):956–966

    Article  MathSciNet  MATH  Google Scholar 

  • Ayaz Fatma (2003) On the two-dimensional differential transform method. Appl Math Comput 143(2):361–374

    Article  MathSciNet  MATH  Google Scholar 

  • Bazeia D, Ashok D, Losano L, Santos MJ (2010) Traveling wave solutions of nonlinear partial differential equations. Appl Math Lett 23(6):681–686

    Article  MathSciNet  MATH  Google Scholar 

  • Bibi Sadaf, Mohyud-Din Syed (2014) Traveling wave solutions of zk-bbm equation sine-cosine method. Commun Num Analy 1–9(03):2014

    MathSciNet  Google Scholar 

  • Che Hussin CH, Kilicman A (2013) Solving system of linear differential equations by using differential transformation method. AIP Conf Proc 1522:245–250

    Article  Google Scholar 

  • Hussin Che Haziqah Che, Kilicman Adem, Mandangan Arif (2010) General differential transformation method for higher order of linear boundary value problem. Borneo Sci 27:35–46

    Google Scholar 

  • Dhaigude Dnyanoba, Birajdar Gunvant, Nikam Vasant (2012) Adomian decomposition method for fractional Benjamin-Bona-Mahony-Burger’s equations. Int J Appl Math Mech 8:02

    Google Scholar 

  • Ertürk VS (2007) Differential transformation method for solving differential equations of lane-emden type. Math Comput Appl 12(3):135–139

    MathSciNet  MATH  Google Scholar 

  • Erturk VS, Momani S (2007) Comparing numerical methods for solving fourth-order boundary value problem. Appl Math Comput 188:1963–1968

    Article  MathSciNet  MATH  Google Scholar 

  • Galdi J, Zhao GP (2014) Exact solitary wave solution in the zk-bbm equation. J Nonlinear Dyn 2356–7503(3):135–139

    Google Scholar 

  • Faghanpour Ganji Hamed, Mohsen Jouya, Abbas Mirhosseini-Amiri Seyed, Domiri Ganji Davod (2016) Traveling wave solution by differential transformation method and reduced differential transformation method. Alexandria Eng J 55(3):2985–2994

    Article  Google Scholar 

  • Hadizadeh M, Moatamedi N (2007) A new differential transformation approach for two-dimensional volterra integral equations. Int J Comput Math 84(4):515–526

    Article  MathSciNet  MATH  Google Scholar 

  • Abdel-Halim Hassan IH (2008) Application to differential transformation method for solving systems of differential equations. Appl Math Model 32(12):2552–2559

    Article  MathSciNet  MATH  Google Scholar 

  • Jafari Hossein, Alipour Maryam, Tajadodi Haleh (2010) Two-dimensional differential transform method for solving nonlinear partial differential equations. Int J Res Rev Appl Sci 2:01

    MATH  Google Scholar 

  • Jiwari Ram, Kumar Vikas, Singh Sukhveer (2022) Lie group analysis, exact solutions and conservation laws to compressible isentropic Navier-Stokes equation. Eng Comput 1–10(38):2027–2036

    Article  Google Scholar 

  • Jiwari Ram, Pandit Sapna, Koksal Mehmet Emir (2019) A class of numerical algorithms based on cubic trigonometric b-spline functions for numerical simulation of nonlinear parabolic problems. Comput Appl Math 38(3):1–22

    Article  MathSciNet  MATH  Google Scholar 

  • Ravi Kanth ASV, Aruna K (2009) Two-dimensional differential transform method for solving linear and non-linear Schrodinger equations. Chaos Solitons Fractals 41(5):2277–2281

    Article  MATH  Google Scholar 

  • Kumar Sanjay, Jiwari Dr Ram, Mittal RC, Awrejcewicz Jan (2021) Dark and bright soliton solutions and computational modeling of nonlinear regularized long wave model. Nonlinear Dyn 104:1–22

    Article  Google Scholar 

  • Hessam Mirgolbabaei, ganji Davood domiri, Taherian H, (2009) Soliton solution of the kadomtse-petviashvili equation by homotopy perturbation method. World J Model Simul 5:1

  • Mirzaee F (2011) Differential transformation method for solving the linear and nonlinear systems of ordinary differential equations. Appl Math Sci 5(70):3465–3472

    MathSciNet  MATH  Google Scholar 

  • Mohyud-Din ST, Yildirim A, Sezer SA, Usman M (2010) (2010) Modified variational iteration method for free-convective boundary-layer equation using padé approximation. Math Prob Eng 5:11

    MATH  Google Scholar 

  • Munganga JMW, Mwambakana JN, Maritz R, Batubenge TA, Moremedi GM (2014) Introduction of the differential transform method to solve differential equations at undergraduate level. Int J Math Educ Sci Technol 45(5):781–794

    Article  MATH  Google Scholar 

  • Odibat Zaid M (2008) Differential transform method for solving volterra integral equation with separable kernels. Math Comput Model 48(7):1144–1149

    Article  MathSciNet  MATH  Google Scholar 

  • Pandit Sapna, Jiwari Ram, Bedi Karan, Koksal Mehmet Emir (2017) Haar wavelets operational matrix based algorithm for computational modelling of hyperbolic type wave equations. Eng Comput 34(8):793–814

    Article  Google Scholar 

  • Patel Arvind, Kumar Vineesh (2018) Dark and kink soliton solutions of the generalized zk-bbm equation by iterative scheme. Chin J Phys 56(3):819–829

    Article  Google Scholar 

  • Rawashdeh Mahmoud, Maitama Shehu (2017) Finding exact solutions of nonlinear pdes using the natural decomposition method. Math Methods Appl Sci 40(1):223–236

    Article  MathSciNet  MATH  Google Scholar 

  • Salahshour S, Allahviranloo T (2013) Application of fuzzy differential transform method for solving fuzzy volterra integral equations. Appl Math Model 37(3):1016–1027

    Article  MathSciNet  MATH  Google Scholar 

  • Sergyeyev A, Skurativskyi S, Vladimirov V (2019) Compacton solutions and (non)integrability of nonlinear evolutionary pdes associated with a chain of prestressed granules. Nonlinear Analy 47:68–84

    Article  MathSciNet  MATH  Google Scholar 

  • Muhammad Shakeel, Tauseef Mohyud-Din Syed (2015) New (g’/g) expansion method and its application to the Zakharov-Kuznetsov-Benjamin-Bona-Mahony (zk-bbm) equation. J Assoc Arab Univ 18(1):66–81

    Google Scholar 

  • Tasbozan O, Kurt A (2015) Approximate analytical solution of zk-bbm equation. Sohag J Math 2:57–60

    Google Scholar 

  • Wazwaz Abdul-Majid (2007) New kinds of solitons and periodic solutions to the generalized kdv equation. Num Methods Part Diff Eq 23(2):247–255

    Article  MathSciNet  MATH  Google Scholar 

  • Yao Guangming, Chen Ching-Shyang, Zheng Hui (2017) A modified method of approximate particular solutions for solving linear and nonlinear pdes. Num Methods Part Diff Eq 33(6):1839–1858

    Article  MathSciNet  MATH  Google Scholar 

  • Yigider M, Karabacak M (2015) The numerical solution of helmholtz equation via multivariate padé approximation. Int J Res Eng Technol 4:670–678

    Article  Google Scholar 

  • Zhang Lina, Huang Wenhua (2019) Breaking wave solutions of a short wave model. Results Phys 15:102733

    Article  Google Scholar 

  • Zhang Xuping, Zhang Jintao, Yu Bo (2020) Finding multiple solutions to elliptic systems with polynomial nonlinearity. Numerical Methods for Partial Differential Equations

  • Zhou X (1986) Differential transformation and its applications for electric circuits. Hauzhong University Press, Wuhan, China 24:1279–1289

    Google Scholar 

  • Zilburg Alon, Rosenau Philip (2019) Early and late stages of k(m, n) compactons interaction. Phys Lett A 383(10):991–996

    Article  MATH  Google Scholar 

Download references

Funding

None.

Author information

Authors and Affiliations

  1. Department of Mathematics, Khawaja Fareed University of Engineering and Information Technology, Rahim Yar Khan, Pakistan

    Nadeem Salamat & Ameer Hamza Arif

  2. Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur, Pakistan

    Muhammad Mustahsan

  3. Department of Computer Science and IT, The Islamia University of Bahawalpur, Bahawalpur, Pakistan

    Malik M. Saad Missen

  4. Department of Electrical Engineering and Computer Science, University of Cincinnati, Cincinnati, OH, 45221, USA

    V. B. Surya Prasath

Authors
  1. Nadeem Salamat
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ameer Hamza Arif
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Muhammad Mustahsan
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Malik M. Saad Missen
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. V. B. Surya Prasath
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All persons who meet authorship criteria are listed as authors, and all authors certify that they have participated sufficiently in the work to take public responsibility for the content, including participation in the concept, design, analysis, writing, or revision of the manuscript. Furthermore, each author certifies that this material or similar material has not been and will not be submitted to or published in any other publication.

Corresponding author

Correspondence to Nadeem Salamat.

Ethics declarations

Conflicts of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

Informed consent

Not applicable.

Additional information

Communicated by Abdellah Hadjadj.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Salamat, N., Arif, A.H., Mustahsan, M. et al. On compacton traveling wave solutions of Zakharov-Kuznetsov-Benjamin-Bona-Mahony (ZK-BBM) equation. Comp. Appl. Math. 41, 365 (2022). https://doi.org/10.1007/s40314-022-02082-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s40314-022-02082-z

Keywords

Mathematics Subject Classification

Search

Navigation