Bell polynomials and lump-type solutions to the Hirota–Satsuma–Ito equation under general and positive quadratic polynomial functions
Tóm tắt
In this article, we explore the Hirota–Satsuma–Ito (HSI) equation in (2+1)-dimensions which possess lump solutions. We first used the concept of Bell’s polynomials to derive the bilinear form of the equation. Then, we proceed to derive a quadratic function solution of the bilinear form and then expand it as the sums of squares of linear functions satisfying some conditions. Most importantly, we acquire a lump-type solution containing 11 parameters along with some non-zero conditions necessary for the existence of the solutions. Then, lump solutions are derived from the from the lump-type solutions by choosing a set of the constant. The solutions obtained in this paper further enrich the literature the ones reported in previous time using different Hirota bilinear approaches and the category of nonlinear partial differential equations (NPDEs) which possess lump solutions, particularly the HSI equation. The physical interpretation of the results is discussed and represented graphically.
Tài liệu tham khảo
citation_title=Linear and Nonlinear Waves; citation_publication_date=1974; citation_id=CR1; citation_author=GB Whitham; citation_publisher=John Whiley
citation_title=Solitons in Optical Communication; citation_publication_date=1995; citation_id=CR2; citation_author=A Hesegawa; citation_author=Y Kodama; citation_publisher=Oxford University Press
citation_journal_title=Computers and Mathematics with Applications; citation_title=Lump-type solutions and lump solutions for the (2+1)-dimensional generalized Bogoyavlensky-Konopelchenko equation; citation_author=Q Li, T Chaolu, YH Wanga; citation_volume=77; citation_publication_date=2019; citation_pages=2077-2085; citation_id=CR3
citation_journal_title=Applied Mathematics Letters; citation_title=General lump-type solutions of the (3+1)-dimensional Jimbo-Miwa equation; citation_author=X Yong, X Li, Y Huang; citation_volume=86; citation_publication_date=2018; citation_pages=222-228; citation_id=CR4
citation_journal_title=Nonlinear Dynam; citation_title=Lump solutions to dimensionally reduced p-gKP and p-gBKP equations; citation_author=WX Ma, ZY Qin, X Lu; citation_volume=84; citation_publication_date=2016; citation_pages=923-931; citation_id=CR5
citation_journal_title=Phys. Lett. A; citation_title=Lump solutions to the Kadomtsev-Petviashvili equation; citation_author=WX Ma; citation_volume=379; citation_publication_date=2015; citation_pages=1975-1978; citation_id=CR6
citation_journal_title=Mod Phys Lett B; citation_title=Lump solutions of a new extended (2 + 1)-dimensionalBoussinesq equation; citation_author=H Wang, YH Wang, WX Ma, C Temuer; citation_volume=32; citation_publication_date=2018; citation_pages=1850376; citation_id=CR7
citation_journal_title=Appl Math Lett; citation_title=Lump and interaction solutions to the (2 + 1)-dimensional Burgers equation; citation_author=H Wang; citation_volume=85; citation_publication_date=2018; citation_pages=27-34; citation_id=CR8
citation_journal_title=Trans. Amer. Math. Soc.; citation_title=Solving the Korteweg-de Vries equation by its bilinear form: Wronskian solutions; citation_author=WX Ma, Y You; citation_volume=357; citation_publication_date=2005; citation_pages=1753-1778; citation_id=CR9
W.X. Ma, A search for lump solutions to a combined fourth-order nonlinear PDE in (2+1)-dimension, Journal of Applied Analysis and Computation. Article in press. 2019. DOI:
https://doi.org/10.11948/*.1
citation_title=Introduction to the Hirota bilinear method; citation_inbook_title=Integrability of Nonlinear Systems; citation_publication_date=1997; citation_pages=95-103; citation_id=CR11; citation_author=J Hietarinta; citation_publisher=Springer
citation_journal_title=Commun Nonlinear Sci Numer Simulat; citation_title=Lump and lump-soliton solutions to the Hirota-Satsuma-Ito equation; citation_author=Y Zhou, S Manukure, WX Ma; citation_volume=68; citation_publication_date=2019; citation_pages=56-62; citation_id=CR12
citation_journal_title=Complexity; citation_title=A Study on Lump Solutions to a Generalized Hirota-Satsuma-Ito Equation in (2+1)-Dimensions; citation_author=WX Ma, J Li, CM Khaliq; citation_volume=2018; citation_publication_date=2018; citation_pages=9059858; citation_id=CR13
citation_journal_title=Ann. Math; citation_title=Exponential polynomials; citation_author=ET Bell; citation_volume=35; citation_publication_date=1934; citation_pages=258-277; citation_id=CR14
citation_journal_title=Modern Physics Letters B; citation_title=On Bell polynomials approach to the integrability of a (3 + 1)-dimensional generalized Kadomtsev Petviashvili equation; citation_author=TT Zhang, PL Ma, MJ Xu, XY Zhang, SF Tian; citation_volume=29; citation_publication_date=2015; citation_pages=1550051; citation_id=CR15
citation_journal_title=Proc. R. Soc. Lond. A; citation_title=On the combinatorics of the Hirota D-operators; citation_author=G Gilson, F Lambert, JJC Nimmo, R Willox; citation_volume=452; citation_publication_date=1996; citation_pages=223-234; citation_id=CR16