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Solitary wave solutions with compact support for the nonlinear dispersive K(m,n) equations by using approximate analytical method

The study of solitons and compactons is important in nonlinear physics. In this paper we combined the Adomian polynomials with the multi-step approach to present a new technique called Multi-step Modified Reduced Differential Transform Method (MMRDTM). The proposed technique has the advantage of pro...

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Main Authors: Che Haziqah Che Hussin, Amirah Azmi, Adem Kilicman
Format: Article
Language:English
English
Published: Penerbit Akademia Baru 2021
Subjects:
QC1-999 Physics
Online Access:https://eprints.ums.edu.my/id/eprint/31332/1/Solitary%20wave%20solutions%20with%20compact%20support%20for%20the%20nonlinear%20dispersive%20k%28m%2Cn%29%20equations%20by%20using%20approximate%20analytical%20method_ABSTRACT.pdf
https://eprints.ums.edu.my/id/eprint/31332/2/Solitary%20wave%20solutions%20with%20compact%20support%20for%20the%20nonlinear%20dispersive%20k%28m%2Cn%29%20equations%20by%20using%20approximate%20analytical%20method.pdf
https://eprints.ums.edu.my/id/eprint/31332/
https://semarakilmu.com.my/journals/index.php/fluid_mechanics_thermal_sciences/article/view/23/8
https://doi.org/10.37934/arfmts.88.1.2434
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spelling my.ums.eprints.313322021-11-30T02:37:10Z https://eprints.ums.edu.my/id/eprint/31332/ Solitary wave solutions with compact support for the nonlinear dispersive K(m,n) equations by using approximate analytical method Che Haziqah Che Hussin Amirah Azmi Adem Kilicman QC1-999 Physics The study of solitons and compactons is important in nonlinear physics. In this paper we combined the Adomian polynomials with the multi-step approach to present a new technique called Multi-step Modified Reduced Differential Transform Method (MMRDTM). The proposed technique has the advantage of producing an analytical approximation in a fast converging sequence with a reduced number of calculated terms. The MMRDTM is presented with some modification of the Reduced Differential Transformation Method (RDTM) with multi-step approach and its nonlinear term is replaced by the Adomian polynomials. Therefore, the nonlinear initial value problem can easily be solved with less computational effort. Besides that, the multi-step approach produces a solution in fast converging series that converges the solution in a wide time area. Two examples are provided to demonstrate the capability and benefits of the proposed method for approximating the solution of NKdVEs with compactons. Graphical inputs are used to represent the solution and to demonstrate the precision and validity of the MMRDTM in graphic illustration. From the results, it was found that it is possible to obtain highly accurate results or exact solutions by using the MMRDTM. Penerbit Akademia Baru 2021 Article PeerReviewed text en https://eprints.ums.edu.my/id/eprint/31332/1/Solitary%20wave%20solutions%20with%20compact%20support%20for%20the%20nonlinear%20dispersive%20k%28m%2Cn%29%20equations%20by%20using%20approximate%20analytical%20method_ABSTRACT.pdf text en https://eprints.ums.edu.my/id/eprint/31332/2/Solitary%20wave%20solutions%20with%20compact%20support%20for%20the%20nonlinear%20dispersive%20k%28m%2Cn%29%20equations%20by%20using%20approximate%20analytical%20method.pdf Che Haziqah Che Hussin and Amirah Azmi and Adem Kilicman (2021) Solitary wave solutions with compact support for the nonlinear dispersive K(m,n) equations by using approximate analytical method. Journal of Advanced Research in Fluid Mechanics and Thermal Sciences, 88. pp. 24-34. ISSN 2289-7879 https://semarakilmu.com.my/journals/index.php/fluid_mechanics_thermal_sciences/article/view/23/8 https://doi.org/10.37934/arfmts.88.1.2434
institution Universiti Malaysia Sabah
building UMS Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Malaysia Sabah
content_source UMS Institutional Repository
url_provider http://eprints.ums.edu.my/
language English
English
topic QC1-999 Physics
spellingShingle QC1-999 Physics
Che Haziqah Che Hussin
Amirah Azmi
Adem Kilicman
Solitary wave solutions with compact support for the nonlinear dispersive K(m,n) equations by using approximate analytical method
description The study of solitons and compactons is important in nonlinear physics. In this paper we combined the Adomian polynomials with the multi-step approach to present a new technique called Multi-step Modified Reduced Differential Transform Method (MMRDTM). The proposed technique has the advantage of producing an analytical approximation in a fast converging sequence with a reduced number of calculated terms. The MMRDTM is presented with some modification of the Reduced Differential Transformation Method (RDTM) with multi-step approach and its nonlinear term is replaced by the Adomian polynomials. Therefore, the nonlinear initial value problem can easily be solved with less computational effort. Besides that, the multi-step approach produces a solution in fast converging series that converges the solution in a wide time area. Two examples are provided to demonstrate the capability and benefits of the proposed method for approximating the solution of NKdVEs with compactons. Graphical inputs are used to represent the solution and to demonstrate the precision and validity of the MMRDTM in graphic illustration. From the results, it was found that it is possible to obtain highly accurate results or exact solutions by using the MMRDTM.
format Article
author Che Haziqah Che Hussin
Amirah Azmi
Adem Kilicman
author_facet Che Haziqah Che Hussin
Amirah Azmi
Adem Kilicman
author_sort Che Haziqah Che Hussin
title Solitary wave solutions with compact support for the nonlinear dispersive K(m,n) equations by using approximate analytical method
title_short Solitary wave solutions with compact support for the nonlinear dispersive K(m,n) equations by using approximate analytical method
title_full Solitary wave solutions with compact support for the nonlinear dispersive K(m,n) equations by using approximate analytical method
title_fullStr Solitary wave solutions with compact support for the nonlinear dispersive K(m,n) equations by using approximate analytical method
title_full_unstemmed Solitary wave solutions with compact support for the nonlinear dispersive K(m,n) equations by using approximate analytical method
title_sort solitary wave solutions with compact support for the nonlinear dispersive k(m,n) equations by using approximate analytical method
publisher Penerbit Akademia Baru
publishDate 2021
url https://eprints.ums.edu.my/id/eprint/31332/1/Solitary%20wave%20solutions%20with%20compact%20support%20for%20the%20nonlinear%20dispersive%20k%28m%2Cn%29%20equations%20by%20using%20approximate%20analytical%20method_ABSTRACT.pdf
https://eprints.ums.edu.my/id/eprint/31332/2/Solitary%20wave%20solutions%20with%20compact%20support%20for%20the%20nonlinear%20dispersive%20k%28m%2Cn%29%20equations%20by%20using%20approximate%20analytical%20method.pdf
https://eprints.ums.edu.my/id/eprint/31332/
https://semarakilmu.com.my/journals/index.php/fluid_mechanics_thermal_sciences/article/view/23/8
https://doi.org/10.37934/arfmts.88.1.2434
_version_ 1760230881505574912
score 13.222552

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