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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10700 - Other natural sciences

Projekt

—

Návaznosti

O - Projekt operacniho programu

Rok uplatnění

2024

Kód důvěrnosti údajů

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

Název periodika

European Physical Journal Plus

ISSN

2190-5444

e-ISSN

—

Svazek periodika

139

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

18

Strana od-do

—

Kód UT WoS článku

001244370100006

EID výsledku v databázi Scopus

2-s2.0-85195373035