A study of self-adjointness, Lie analysis, wave structures, and conservation laws of the completely generalized shallow water equation

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27740%2F24%3A10255149" target="_blank" >RIV/61989100:27740/24:10255149 - isvavai.cz</a>

Result on the web

<a href="https://link.springer.com/article/10.1140/epjp/s13360-024-05310-z" target="_blank" >https://link.springer.com/article/10.1140/epjp/s13360-024-05310-z</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1140/epjp/s13360-024-05310-z" target="_blank" >10.1140/epjp/s13360-024-05310-z</a>

Result language

angličtina

Original language name

A study of self-adjointness, Lie analysis, wave structures, and conservation laws of the completely generalized shallow water equation

Original language description

This article explores the analysis of the completely generalized Hirota-Satsuma-Ito equation through Lie symmetry analysis. The equation under consideration represents a more comprehensive form of the (2+1)-dimensional HSI equation, encompassing four additional second-order derivative terms: Delta 3 H Pi Pi documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$Delta _{3}H_{varpi varpi }$$end{document} , Delta 4 H Pi iota documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$Delta _{4}H_{varpi iota }$$end{document} , Delta 3 H Pi Pi documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$Delta _{3}H_{varpi varpi }$$end{document} , Delta 4 H Pi iota documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$Delta _{4}H_{varpi iota }$$end{document} , and Delta 6 H iota iota documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$Delta _{6}H_{iota iota }$$end{document} , emerging from the inclusion of second-order dissipative-type elements. We calculate the infinitesimal generators and determine the symmetry group for each generator using the Lie group invariance condition. Employing the conjugacy classes of the Abelian algebra, we transform the considered equation into an ordinary differential equation through similarity reduction. Subsequently, we solve these ordinary differential equations to derive closed-form solutions for the completely generalized Hirota-Satsuma-Ito equation under certain conditions. For other scenarios, we utilize the extended direct algebraic method to obtain soliton solutions. Furthermore, we rigorously calculated the conserved quantities corresponding to each symmetry generator, the conservation laws of the model are established using the multiplier approach. Additionally, we present the graphical representation of selected solutions for specific values of the physical parameters of the equation under scrutiny.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10700 - Other natural sciences

Project

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Continuities

O - Projekt operacniho programu

Publication year

2024

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

European Physical Journal Plus

ISSN

2190-5444

e-ISSN

—

Volume of the periodical

139

Issue of the periodical within the volume

6

Country of publishing house

DE - GERMANY

Number of pages

18

Pages from-to

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UT code for WoS article

001244370100006

EID of the result in the Scopus database

2-s2.0-85195373035