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Teoreticheskaya i Matematicheskaya Fizika, 2018, Volume 197, Number 1, Pages 3–23
DOI: https://doi.org/10.4213/tmf9483
(Mi tmf9483)
 

This article is cited in 24 scientific papers (total in 24 papers)

Conservation laws, symmetries, and line soliton solutions of generalized KP and Boussinesq equations with p-power nonlinearities in two dimensions

S. C. Ancoa, M. L. Gandariasb, E. Reciob

a Brock University, St. Catharines, Canada
b Cadiz University, Cadiz, Spain
References:
Abstract: Nonlinear generalizations of integrable equations in one dimension, such as the Korteweg–de Vries and Boussinesq equations with p-power nonlinearities, arise in many physical applications and are interesting from the analytic standpoint because of their critical behavior. We study analogous nonlinear p-power generalizations of the integrable Kadomtsev–Petviashvili and Boussinesq equations in two dimensions. For all p0, we present a Hamiltonian formulation of these two generalized equations. We derive all Lie symmetries including those that exist for special powers p0. We use Noether's theorem to obtain conservation laws arising from the variational Lie symmetries. Finally, we obtain explicit line soliton solutions for all powers p>0 and discuss some of their properties.
Keywords: line soliton, conservation law, Kadomtsev–Petviashvili equation.
Funding agency Grant number
Natural Sciences and Engineering Research Council of Canada (NSERC)
The research of S. C. Anco is supported by an NSERC research grant.
Received: 10.10.2017
English version:
Theoretical and Mathematical Physics, 2018, Volume 197, Issue 1, Pages 1393–1411
DOI: https://doi.org/10.1134/S004057791810001X
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: S. C. Anco, M. L. Gandarias, E. Recio, “Conservation laws, symmetries, and line soliton solutions of generalized KP and Boussinesq equations with p-power nonlinearities in two dimensions”, TMF, 197:1 (2018), 3–23; Theoret. and Math. Phys., 197:1 (2018), 1393–1411
Citation in format AMSBIB
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Linking options:
  • https://www.mathnet.ru/eng/tmf9483
  • https://doi.org/10.4213/tmf9483
  • https://www.mathnet.ru/eng/tmf/v197/i1/p3
  • This publication is cited in the following 24 articles:
    1. Almudena P. Márquez, Tamara M. Garrido, Chaudry Masood Khalique, María L. Gandarias, “Symmetries, conservation laws, and line soliton solutions of a two-dimensional generalized KdV equation with $ p $-power”, DCDS-S, 2024  crossref
    2. N. Serikbayev, A. Saparbekova, “Symmetry and conservation laws of the (2+1)-dimensional nonlinear Schrödinger-type equation”, Int. J. Geom. Methods Mod. Phys., 20:10 (2023), 2350172  crossref  mathscinet
    3. J. A. Alvarez-Valdez, G. Fernandez-Anaya, “Roadmap of the multiplier method for partial differential equations”, Mathematics, 11:22 (2023), 4572  crossref
    4. M. Jafari, S. Mahdion, A. Akgül, S. M. Eldin, “New conservation laws of the Boussinesq and generalized Kadomtsev–Petviashvili equations via homotopy operator”, Results in Physics, 47 (2023), 106369  crossref
    5. L. Ju, J. Zhou, Y. Zhang, “Conservation laws analysis of nonlinear partial differential equations and their linear soliton solutions and Hamiltonian structures”, Communications in Analysis and Mechanics, 15:2 (2023), 24  crossref  mathscinet
    6. M. Rosa, M.L. Gandarias, A. Niño-López, S. Chulián, “Exact solutions through symmetry reductions for a high-grade brain tumor model with response to hypoxia”, Chaos, Solitons & Fractals, 171 (2023), 113468  crossref  mathscinet
    7. S. J. Ryskamp, M. A. Hoefer, G. Biondini, “Modulation theory for soliton resonance and Mach reflection”, Proc. R. Soc. A, 478:2259 (2022)  crossref  mathscinet
    8. A. Iqbal, I. Naeem, “Conservation laws and exact solutions of a generalized Kadomtsev–Petviashvili (KP)-like equation”, Math. Methods in App. Sciences, 45:17 (2022), 11206  crossref  mathscinet
    9. S. C. Anco, E. Recio, “Topological charges and conservation laws involving an arbitrary function of time for dynamical PDEs”, Proc. R. Soc. A-Math. Phys. Eng. Sci., 477:2245 (2021), 20200442  crossref  mathscinet  isi  scopus
    10. S. C. Anco, M. L. Gandarias, E. Recio, “Line-solitons, line-shocks, and conservation laws of a universal kp-like equation in 2+1 dimensions”, J. Math. Anal. Appl., 504:1 (2021), 125319  crossref  mathscinet  isi
    11. G. R. Deffo, S. B. Yamgoue, T. F. Fozin, F. B. Pelap, “Bifurcation of gap solitary waves in a two-dimensional electrical network with nonlinear dispersion”, Chaos Solitons Fractals, 144 (2021), 110630  crossref  mathscinet  isi
    12. F. B. Pelap, J. E. Ndecfo, G. R. Deffo, “Hybrid behavior of a two-dimensional noguchi nonlinear electrical network”, Phys. Scr., 96:7 (2021), 075211  crossref  isi
    13. S. C. Anco, B. Wang, “A formula for symmetry recursion operators from non-variational symmetries of partial differential equations”, Lett. Math. Phys., 111:3 (2021), 70  crossref  mathscinet  isi
    14. S. A. T. Fonkoua, F. B. Pelap, G. R. Deffo, A. Fomethe, “Rogue wave signals in a coupled anharmonic network: effects of the transverse direction”, Eur. Phys. J. Plus, 136:4 (2021), 416  crossref  isi
    15. Acharya S.P., Mukherjee A., Janaki M.S., “Accelerated Magnetosonic Lump Wave Solutions By Orbiting Charged Space Debris”, Nonlinear Dyn., 105:1 (2021), 671–689  crossref  isi
    16. Feng Zhang, Yuru Hu, Xiangpeng Xin, Stephen C. Anco, “Lie Symmetry Analysis, Exact Solutions, and Conservation Laws of Variable-Coefficients Boiti-Leon-Pempinelli Equation”, Advances in Mathematical Physics, 2021 (2021), 1  crossref  mathscinet
    17. de la Rosa R., Recio E., Garrido T.M., Bruzon M.S., “Lie Symmetry Analysis of (2+1)-Dimensional Kdv Equations With Variable Coefficients”, Int. J. Comput. Math., 97:1-2 (2020), 330–340  crossref  mathscinet  isi  scopus
    18. S. C. Anco, M. L. Gandarias, “Symmetry multi-reduction method for partial differential equations with conservation laws”, Commun. Nonlinear Sci. Numer. Simul., 91 (2020), 105349  crossref  mathscinet  zmath  isi  scopus
    19. S. C. Anco, M. Luz Gandarias, E. Recio, “Conservation laws and line soliton solutions of a family of modified kp equations”, Discret. Contin. Dyn. Syst.-Ser. S, 13:10, SI (2020), 2655–2665  crossref  mathscinet  zmath  isi  scopus
    20. M. Luz Gandarias, M. Rosa Duran, Ch. Masood Khalique, “Conservation laws and travelling wave solutions for double dispersion equations in (1+1) and (2+1) dimensions”, Symmetry-Basel, 12:6 (2020), 950  crossref  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теоретическая и математическая физика Theoretical and Mathematical Physics
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